diff --git a/docs/mkdocs/docs/api/basic_json/to_bson.md b/docs/mkdocs/docs/api/basic_json/to_bson.md
index 786fbc9e0..4cd45a57d 100644
--- a/docs/mkdocs/docs/api/basic_json/to_bson.md
+++ b/docs/mkdocs/docs/api/basic_json/to_bson.md
@@ -46,9 +46,8 @@ Strong guarantee: if an exception is thrown, there are no changes in the JSON va
 
 ## Complexity
 
-Proportional to the size of the JSON value `j` multiplied by its maximum nesting
-depth, `O(n × d)`. BSON length prefixes are computed recursively before nested
-values are written.
+Linear in the size of the JSON value `j`. The length prefixes of all nested documents and arrays are computed in one
+pass before anything is written.
 
 ## Examples
 
@@ -77,3 +76,4 @@ values are written.
 ## Version history
 
 - Added in version 3.4.0.
+- Linear in the size of `j`, and no longer limited by the call stack for deeply nested values, since version 3.13.0.
diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index a355f1c15..a9291bcbd 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -122,7 +122,7 @@ class binary_writer
         {
             case value_t::object:
             {
-                write_bson_object(*j.m_data.m_value.object);
+                write_bson_document(j);
                 break;
             }
 
@@ -1201,35 +1201,6 @@ class binary_writer
         }
     }
 
-    /*!
-    @brief Writes a BSON element with key @a name and object @a value
-    */
-    void write_bson_object_entry(const string_t& name,
-                                 const typename BasicJsonType::object_t& value)
-    {
-        write_bson_entry_header(name, 0x03); // object
-        write_bson_object(value);
-    }
-
-    /*!
-    @return The size of the BSON-encoded array @a value
-    */
-    static std::size_t calc_bson_array_size(const typename BasicJsonType::array_t& value)
-    {
-        std::size_t array_index = 0ul;
-
-        const std::size_t embedded_document_size = std::accumulate(std::begin(value), std::end(value), static_cast<std::size_t>(0), [&array_index](std::size_t result, const typename BasicJsonType::array_t::value_type & el)
-        {
-            // the index is built as a std::string, while calc_bson_element_size
-            // takes a string_t; convert explicitly, as the two are only
-            // implicitly convertible for some string types
-            const auto key = std::to_string(array_index++);
-            return result + calc_bson_element_size(string_t(key.data(), key.size()), el);
-        });
-
-        return sizeof(std::int32_t) + embedded_document_size + 1ul;
-    }
-
     /*!
     @return The size of the BSON-encoded binary array @a value
     */
@@ -1238,29 +1209,6 @@ class binary_writer
         return sizeof(std::int32_t) + value.size() + 1ul;
     }
 
-    /*!
-    @brief Writes a BSON element with key @a name and array @a value
-    */
-    void write_bson_array(const string_t& name,
-                          const typename BasicJsonType::array_t& value)
-    {
-        write_bson_entry_header(name, 0x04); // array
-        write_number<std::int32_t>(to_bson_length(calc_bson_array_size(value)), true);
-
-        std::size_t array_index = 0ul;
-
-        for (const auto& el : value)
-        {
-            // the index is built as a std::string, while write_bson_element takes
-            // a string_t; convert explicitly, as the two are only implicitly
-            // convertible for some string types
-            const auto key = std::to_string(array_index++);
-            write_bson_element(string_t(key.data(), key.size()), el);
-        }
-
-        oa.write_character(to_char_type(0x00));
-    }
-
     /*!
     @brief Writes a BSON element with key @a name and binary value @a value
     */
@@ -1282,43 +1230,37 @@ class binary_writer
     }
 
     /*!
-    @brief Calculates the size necessary to serialize the JSON value @a j with its @a name
-    @return The calculated size for the BSON document entry for @a j with the given @a name.
+    @return The size of the value of the BSON document entry for @a j, which
+            is neither an object nor an array
     */
-    static std::size_t calc_bson_element_size(const string_t& name,
-            const BasicJsonType& j)
+    static std::size_t calc_bson_value_size(const BasicJsonType& j)
     {
-        const auto header_size = calc_bson_entry_header_size(name, j);
         switch (j.type())
         {
-            case value_t::object:
-                return header_size + calc_bson_object_size(*j.m_data.m_value.object);
-
-            case value_t::array:
-                return header_size + calc_bson_array_size(*j.m_data.m_value.array);
-
             case value_t::binary:
-                return header_size + calc_bson_binary_size(*j.m_data.m_value.binary);
+                return calc_bson_binary_size(*j.m_data.m_value.binary);
 
             case value_t::boolean:
-                return header_size + 1ul;
+                return 1ul;
 
             case value_t::number_float:
-                return header_size + 8ul;
+                return 8ul;
 
             case value_t::number_integer:
-                return header_size + calc_bson_integer_size(j.m_data.m_value.number_integer);
+                return calc_bson_integer_size(j.m_data.m_value.number_integer);
 
             case value_t::number_unsigned:
-                return header_size + calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
+                return calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
 
             case value_t::string:
-                return header_size + calc_bson_string_size(*j.m_data.m_value.string);
+                return calc_bson_string_size(*j.m_data.m_value.string);
 
             case value_t::null:
-                return header_size + 0ul;
+                return 0ul;
 
             // LCOV_EXCL_START
+            case value_t::object:
+            case value_t::array:
             case value_t::discarded:
             default:
                 JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
@@ -1328,22 +1270,13 @@ class binary_writer
     }
 
     /*!
-    @brief Serializes the JSON value @a j to BSON and associates it with the
-           key @a name.
-    @param name The name to associate with the JSON entity @a j within the
-                current BSON document
+    @brief Writes the BSON document entry with key @a name for @a j, which is
+           neither an object nor an array
     */
-    void write_bson_element(const string_t& name,
-                            const BasicJsonType& j)
+    void write_bson_value(const string_t& name, const BasicJsonType& j)
     {
         switch (j.type())
         {
-            case value_t::object:
-                return write_bson_object_entry(name, *j.m_data.m_value.object);
-
-            case value_t::array:
-                return write_bson_array(name, *j.m_data.m_value.array);
-
             case value_t::binary:
                 return write_bson_binary(name, *j.m_data.m_value.binary);
 
@@ -1366,6 +1299,8 @@ class binary_writer
                 return write_bson_null(name);
 
             // LCOV_EXCL_START
+            case value_t::object:
+            case value_t::array:
             case value_t::discarded:
             default:
                 JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
@@ -1374,37 +1309,219 @@ class binary_writer
         }
     }
 
-    /*!
-    @brief Calculates the size of the BSON serialization of the given
-           JSON-object @a j.
-    @param[in] value  JSON value to serialize
-    @pre       value.type() == value_t::object
-    */
-    static std::size_t calc_bson_object_size(const typename BasicJsonType::object_t& value)
+    /// @brief an object or array of the BSON document being sized or written
+    struct bson_frame
     {
-        const std::size_t document_size = std::accumulate(value.begin(), value.end(), static_cast<std::size_t>(0),
-                                          [](size_t result, const typename BasicJsonType::object_t::value_type & el)
+        explicit bson_frame(const BasicJsonType* value_, const std::size_t size_slot_ = 0)
+            : value(value_)
+            , size_slot(size_slot_)
         {
-            return result += calc_bson_element_size(el.first, el.second);
-        });
+            if (value->is_object())
+            {
+                member = value->m_data.m_value.object->cbegin();
+            }
+        }
 
-        return sizeof(std::int32_t) + document_size + 1ul;
+        /// the object or array
+        const BasicJsonType* value;
+        /// objects: the next member
+        typename BasicJsonType::object_t::const_iterator member{};
+        /// arrays: the index of the next element
+        std::size_t index = 0;
+        /// @ref calc_bson_sizes only: where its size goes in the table
+        std::size_t size_slot;
+        /// @ref calc_bson_sizes only: the size of its entries seen so far
+        std::size_t entries_size = 0;
+    };
+
+    /*!
+    @brief the name BSON gives the array element with index @a index
+    @param[out] name  receives the decimal index
+    */
+    static const string_t& bson_index_name(const std::size_t index, string_t& name)
+    {
+        // the index is built as a std::string; convert explicitly, as the
+        // two are only implicitly convertible for some string types
+        const auto key = std::to_string(index);
+        name = string_t(key.data(), key.size());
+        return name;
     }
 
     /*!
-    @param[in] value  JSON value to serialize
-    @pre       value.type() == value_t::object
+    @brief Calculates the size of every object and array in the BSON document
+           @a document, including the document itself.
+
+    BSON prefixes every document and array with its size, so all of them have
+    to be known before the first byte is written. They are computed in a
+    single pass, each one from the sizes of its entries, which keeps
+    serializing linear in the size of the document; computing each size by
+    walking the entire value below it made it quadratic in the nesting depth.
+    The pass keeps the objects and arrays it has entered on an explicit stack,
+    so a deeply nested value cannot exhaust the call stack.
+
+    @param[in] document  the JSON object to serialize
+    @param[out] nested_sizes  the sizes of the objects and arrays in
+                              @a document, in the order they are written
+    @return the size of @a document
+    @throw out_of_range.409 if a key contains U+0000, before anything is
+           written
     */
-    void write_bson_object(const typename BasicJsonType::object_t& value)
+    static std::size_t calc_bson_sizes(const BasicJsonType& document, std::vector<std::size_t>& nested_sizes)
     {
-        write_number<std::int32_t>(to_bson_length(calc_bson_object_size(value)), true);
+        // the object or array whose entries are being sized, and the ones it
+        // is in; nothing is allocated unless the document nests
+        bson_frame current(&document);
+        std::vector<bson_frame> parents;
+        string_t index_name;
 
-        for (const auto& el : value)
+        while (true)
         {
-            write_bson_element(el.first, el.second);
-        }
+            // size entries until the current object or array is done, or an
+            // entry is an object or array itself
+            const BasicJsonType* nested = nullptr;
+            if (current.value->is_object())
+            {
+                const auto& object = *current.value->m_data.m_value.object;
+                while (nested == nullptr && current.member != object.cend())
+                {
+                    const auto& el = *current.member;
+                    ++current.member;
+                    current.entries_size += calc_bson_entry_header_size(el.first, el.second);
+                    if (el.second.is_structured())
+                    {
+                        nested = &el.second;
+                    }
+                    else
+                    {
+                        current.entries_size += calc_bson_value_size(el.second);
+                    }
+                }
+            }
+            else
+            {
+                const auto& array = *current.value->m_data.m_value.array;
+                while (nested == nullptr && current.index < array.size())
+                {
+                    const BasicJsonType& el = array[current.index];
+                    current.entries_size += calc_bson_entry_header_size(bson_index_name(current.index, index_name), el);
+                    ++current.index;
+                    if (el.is_structured())
+                    {
+                        nested = &el;
+                    }
+                    else
+                    {
+                        current.entries_size += calc_bson_value_size(el);
+                    }
+                }
+            }
 
-        oa.write_character(to_char_type(0x00));
+            if (nested != nullptr)
+            {
+                // its size is added to the current one's once it is done
+                nested_sizes.push_back(0);
+                parents.push_back(std::move(current));
+                current = bson_frame(nested, nested_sizes.size() - 1);
+                continue;
+            }
+
+            // the int32 size, the entries, and the terminating null byte
+            const std::size_t size = sizeof(std::int32_t) + current.entries_size + 1ul;
+            if (parents.empty())
+            {
+                return size;
+            }
+            nested_sizes[current.size_slot] = size;
+            current = std::move(parents.back());
+            parents.pop_back();
+            current.entries_size += size;
+        }
+    }
+
+    /*!
+    @brief Serializes the JSON object @a document as a BSON document
+
+    Writes the objects and arrays in it without the call stack, keeping the
+    ones it has entered on an explicit stack, so a deeply nested value
+    cannot exhaust the call stack.
+
+    @param[in] document  the JSON object to serialize
+    @pre       document.type() == value_t::object
+    */
+    void write_bson_document(const BasicJsonType& document)
+    {
+        std::vector<std::size_t> nested_sizes;
+        const std::size_t document_size = calc_bson_sizes(document, nested_sizes);
+        write_number<std::int32_t>(to_bson_length(document_size), true);
+
+        // the object or array whose entries are being written, and the ones
+        // it is in
+        bson_frame current(&document);
+        std::vector<bson_frame> parents;
+        std::size_t next_size = 0;
+        string_t index_name;
+
+        while (true)
+        {
+            // write entries until the current object or array is done, or an
+            // entry is an object or array itself
+            const string_t* nested_name = nullptr;
+            const BasicJsonType* nested = nullptr;
+            if (current.value->is_object())
+            {
+                const auto& object = *current.value->m_data.m_value.object;
+                while (nested == nullptr && current.member != object.cend())
+                {
+                    const auto& el = *current.member;
+                    ++current.member;
+                    if (el.second.is_structured())
+                    {
+                        nested_name = &el.first;
+                        nested = &el.second;
+                    }
+                    else
+                    {
+                        write_bson_value(el.first, el.second);
+                    }
+                }
+            }
+            else
+            {
+                const auto& array = *current.value->m_data.m_value.array;
+                while (nested == nullptr && current.index < array.size())
+                {
+                    const BasicJsonType& el = array[current.index];
+                    const string_t& name = bson_index_name(current.index, index_name);
+                    ++current.index;
+                    if (el.is_structured())
+                    {
+                        nested_name = &name;
+                        nested = &el;
+                    }
+                    else
+                    {
+                        write_bson_value(name, el);
+                    }
+                }
+            }
+
+            if (nested != nullptr)
+            {
+                write_bson_entry_header(*nested_name, nested->is_object() ? 0x03 : 0x04);
+                write_number<std::int32_t>(to_bson_length(nested_sizes[next_size++]), true);
+                parents.push_back(std::move(current));
+                current = bson_frame(nested);
+                continue;
+            }
+
+            oa.write_character(to_char_type(0x00));
+            if (parents.empty())
+            {
+                return;
+            }
+            current = std::move(parents.back());
+            parents.pop_back();
+        }
     }
 
     //////////
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index c96461458..b94841147 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -19084,7 +19084,7 @@ class binary_writer
         {
             case value_t::object:
             {
-                write_bson_object(*j.m_data.m_value.object);
+                write_bson_document(j);
                 break;
             }
 
@@ -20163,35 +20163,6 @@ class binary_writer
         }
     }
 
-    /*!
-    @brief Writes a BSON element with key @a name and object @a value
-    */
-    void write_bson_object_entry(const string_t& name,
-                                 const typename BasicJsonType::object_t& value)
-    {
-        write_bson_entry_header(name, 0x03); // object
-        write_bson_object(value);
-    }
-
-    /*!
-    @return The size of the BSON-encoded array @a value
-    */
-    static std::size_t calc_bson_array_size(const typename BasicJsonType::array_t& value)
-    {
-        std::size_t array_index = 0ul;
-
-        const std::size_t embedded_document_size = std::accumulate(std::begin(value), std::end(value), static_cast<std::size_t>(0), [&array_index](std::size_t result, const typename BasicJsonType::array_t::value_type & el)
-        {
-            // the index is built as a std::string, while calc_bson_element_size
-            // takes a string_t; convert explicitly, as the two are only
-            // implicitly convertible for some string types
-            const auto key = std::to_string(array_index++);
-            return result + calc_bson_element_size(string_t(key.data(), key.size()), el);
-        });
-
-        return sizeof(std::int32_t) + embedded_document_size + 1ul;
-    }
-
     /*!
     @return The size of the BSON-encoded binary array @a value
     */
@@ -20200,29 +20171,6 @@ class binary_writer
         return sizeof(std::int32_t) + value.size() + 1ul;
     }
 
-    /*!
-    @brief Writes a BSON element with key @a name and array @a value
-    */
-    void write_bson_array(const string_t& name,
-                          const typename BasicJsonType::array_t& value)
-    {
-        write_bson_entry_header(name, 0x04); // array
-        write_number<std::int32_t>(to_bson_length(calc_bson_array_size(value)), true);
-
-        std::size_t array_index = 0ul;
-
-        for (const auto& el : value)
-        {
-            // the index is built as a std::string, while write_bson_element takes
-            // a string_t; convert explicitly, as the two are only implicitly
-            // convertible for some string types
-            const auto key = std::to_string(array_index++);
-            write_bson_element(string_t(key.data(), key.size()), el);
-        }
-
-        oa.write_character(to_char_type(0x00));
-    }
-
     /*!
     @brief Writes a BSON element with key @a name and binary value @a value
     */
@@ -20244,43 +20192,37 @@ class binary_writer
     }
 
     /*!
-    @brief Calculates the size necessary to serialize the JSON value @a j with its @a name
-    @return The calculated size for the BSON document entry for @a j with the given @a name.
+    @return The size of the value of the BSON document entry for @a j, which
+            is neither an object nor an array
     */
-    static std::size_t calc_bson_element_size(const string_t& name,
-            const BasicJsonType& j)
+    static std::size_t calc_bson_value_size(const BasicJsonType& j)
     {
-        const auto header_size = calc_bson_entry_header_size(name, j);
         switch (j.type())
         {
-            case value_t::object:
-                return header_size + calc_bson_object_size(*j.m_data.m_value.object);
-
-            case value_t::array:
-                return header_size + calc_bson_array_size(*j.m_data.m_value.array);
-
             case value_t::binary:
-                return header_size + calc_bson_binary_size(*j.m_data.m_value.binary);
+                return calc_bson_binary_size(*j.m_data.m_value.binary);
 
             case value_t::boolean:
-                return header_size + 1ul;
+                return 1ul;
 
             case value_t::number_float:
-                return header_size + 8ul;
+                return 8ul;
 
             case value_t::number_integer:
-                return header_size + calc_bson_integer_size(j.m_data.m_value.number_integer);
+                return calc_bson_integer_size(j.m_data.m_value.number_integer);
 
             case value_t::number_unsigned:
-                return header_size + calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
+                return calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
 
             case value_t::string:
-                return header_size + calc_bson_string_size(*j.m_data.m_value.string);
+                return calc_bson_string_size(*j.m_data.m_value.string);
 
             case value_t::null:
-                return header_size + 0ul;
+                return 0ul;
 
             // LCOV_EXCL_START
+            case value_t::object:
+            case value_t::array:
             case value_t::discarded:
             default:
                 JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
@@ -20290,22 +20232,13 @@ class binary_writer
     }
 
     /*!
-    @brief Serializes the JSON value @a j to BSON and associates it with the
-           key @a name.
-    @param name The name to associate with the JSON entity @a j within the
-                current BSON document
+    @brief Writes the BSON document entry with key @a name for @a j, which is
+           neither an object nor an array
     */
-    void write_bson_element(const string_t& name,
-                            const BasicJsonType& j)
+    void write_bson_value(const string_t& name, const BasicJsonType& j)
     {
         switch (j.type())
         {
-            case value_t::object:
-                return write_bson_object_entry(name, *j.m_data.m_value.object);
-
-            case value_t::array:
-                return write_bson_array(name, *j.m_data.m_value.array);
-
             case value_t::binary:
                 return write_bson_binary(name, *j.m_data.m_value.binary);
 
@@ -20328,6 +20261,8 @@ class binary_writer
                 return write_bson_null(name);
 
             // LCOV_EXCL_START
+            case value_t::object:
+            case value_t::array:
             case value_t::discarded:
             default:
                 JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
@@ -20336,37 +20271,219 @@ class binary_writer
         }
     }
 
-    /*!
-    @brief Calculates the size of the BSON serialization of the given
-           JSON-object @a j.
-    @param[in] value  JSON value to serialize
-    @pre       value.type() == value_t::object
-    */
-    static std::size_t calc_bson_object_size(const typename BasicJsonType::object_t& value)
+    /// @brief an object or array of the BSON document being sized or written
+    struct bson_frame
     {
-        const std::size_t document_size = std::accumulate(value.begin(), value.end(), static_cast<std::size_t>(0),
-                                          [](size_t result, const typename BasicJsonType::object_t::value_type & el)
+        explicit bson_frame(const BasicJsonType* value_, const std::size_t size_slot_ = 0)
+            : value(value_)
+            , size_slot(size_slot_)
         {
-            return result += calc_bson_element_size(el.first, el.second);
-        });
+            if (value->is_object())
+            {
+                member = value->m_data.m_value.object->cbegin();
+            }
+        }
 
-        return sizeof(std::int32_t) + document_size + 1ul;
+        /// the object or array
+        const BasicJsonType* value;
+        /// objects: the next member
+        typename BasicJsonType::object_t::const_iterator member{};
+        /// arrays: the index of the next element
+        std::size_t index = 0;
+        /// @ref calc_bson_sizes only: where its size goes in the table
+        std::size_t size_slot;
+        /// @ref calc_bson_sizes only: the size of its entries seen so far
+        std::size_t entries_size = 0;
+    };
+
+    /*!
+    @brief the name BSON gives the array element with index @a index
+    @param[out] name  receives the decimal index
+    */
+    static const string_t& bson_index_name(const std::size_t index, string_t& name)
+    {
+        // the index is built as a std::string; convert explicitly, as the
+        // two are only implicitly convertible for some string types
+        const auto key = std::to_string(index);
+        name = string_t(key.data(), key.size());
+        return name;
     }
 
     /*!
-    @param[in] value  JSON value to serialize
-    @pre       value.type() == value_t::object
+    @brief Calculates the size of every object and array in the BSON document
+           @a document, including the document itself.
+
+    BSON prefixes every document and array with its size, so all of them have
+    to be known before the first byte is written. They are computed in a
+    single pass, each one from the sizes of its entries, which keeps
+    serializing linear in the size of the document; computing each size by
+    walking the entire value below it made it quadratic in the nesting depth.
+    The pass keeps the objects and arrays it has entered on an explicit stack,
+    so a deeply nested value cannot exhaust the call stack.
+
+    @param[in] document  the JSON object to serialize
+    @param[out] nested_sizes  the sizes of the objects and arrays in
+                              @a document, in the order they are written
+    @return the size of @a document
+    @throw out_of_range.409 if a key contains U+0000, before anything is
+           written
     */
-    void write_bson_object(const typename BasicJsonType::object_t& value)
+    static std::size_t calc_bson_sizes(const BasicJsonType& document, std::vector<std::size_t>& nested_sizes)
     {
-        write_number<std::int32_t>(to_bson_length(calc_bson_object_size(value)), true);
+        // the object or array whose entries are being sized, and the ones it
+        // is in; nothing is allocated unless the document nests
+        bson_frame current(&document);
+        std::vector<bson_frame> parents;
+        string_t index_name;
 
-        for (const auto& el : value)
+        while (true)
         {
-            write_bson_element(el.first, el.second);
-        }
+            // size entries until the current object or array is done, or an
+            // entry is an object or array itself
+            const BasicJsonType* nested = nullptr;
+            if (current.value->is_object())
+            {
+                const auto& object = *current.value->m_data.m_value.object;
+                while (nested == nullptr && current.member != object.cend())
+                {
+                    const auto& el = *current.member;
+                    ++current.member;
+                    current.entries_size += calc_bson_entry_header_size(el.first, el.second);
+                    if (el.second.is_structured())
+                    {
+                        nested = &el.second;
+                    }
+                    else
+                    {
+                        current.entries_size += calc_bson_value_size(el.second);
+                    }
+                }
+            }
+            else
+            {
+                const auto& array = *current.value->m_data.m_value.array;
+                while (nested == nullptr && current.index < array.size())
+                {
+                    const BasicJsonType& el = array[current.index];
+                    current.entries_size += calc_bson_entry_header_size(bson_index_name(current.index, index_name), el);
+                    ++current.index;
+                    if (el.is_structured())
+                    {
+                        nested = &el;
+                    }
+                    else
+                    {
+                        current.entries_size += calc_bson_value_size(el);
+                    }
+                }
+            }
 
-        oa.write_character(to_char_type(0x00));
+            if (nested != nullptr)
+            {
+                // its size is added to the current one's once it is done
+                nested_sizes.push_back(0);
+                parents.push_back(std::move(current));
+                current = bson_frame(nested, nested_sizes.size() - 1);
+                continue;
+            }
+
+            // the int32 size, the entries, and the terminating null byte
+            const std::size_t size = sizeof(std::int32_t) + current.entries_size + 1ul;
+            if (parents.empty())
+            {
+                return size;
+            }
+            nested_sizes[current.size_slot] = size;
+            current = std::move(parents.back());
+            parents.pop_back();
+            current.entries_size += size;
+        }
+    }
+
+    /*!
+    @brief Serializes the JSON object @a document as a BSON document
+
+    Writes the objects and arrays in it without the call stack, keeping the
+    ones it has entered on an explicit stack, so a deeply nested value
+    cannot exhaust the call stack.
+
+    @param[in] document  the JSON object to serialize
+    @pre       document.type() == value_t::object
+    */
+    void write_bson_document(const BasicJsonType& document)
+    {
+        std::vector<std::size_t> nested_sizes;
+        const std::size_t document_size = calc_bson_sizes(document, nested_sizes);
+        write_number<std::int32_t>(to_bson_length(document_size), true);
+
+        // the object or array whose entries are being written, and the ones
+        // it is in
+        bson_frame current(&document);
+        std::vector<bson_frame> parents;
+        std::size_t next_size = 0;
+        string_t index_name;
+
+        while (true)
+        {
+            // write entries until the current object or array is done, or an
+            // entry is an object or array itself
+            const string_t* nested_name = nullptr;
+            const BasicJsonType* nested = nullptr;
+            if (current.value->is_object())
+            {
+                const auto& object = *current.value->m_data.m_value.object;
+                while (nested == nullptr && current.member != object.cend())
+                {
+                    const auto& el = *current.member;
+                    ++current.member;
+                    if (el.second.is_structured())
+                    {
+                        nested_name = &el.first;
+                        nested = &el.second;
+                    }
+                    else
+                    {
+                        write_bson_value(el.first, el.second);
+                    }
+                }
+            }
+            else
+            {
+                const auto& array = *current.value->m_data.m_value.array;
+                while (nested == nullptr && current.index < array.size())
+                {
+                    const BasicJsonType& el = array[current.index];
+                    const string_t& name = bson_index_name(current.index, index_name);
+                    ++current.index;
+                    if (el.is_structured())
+                    {
+                        nested_name = &name;
+                        nested = &el;
+                    }
+                    else
+                    {
+                        write_bson_value(name, el);
+                    }
+                }
+            }
+
+            if (nested != nullptr)
+            {
+                write_bson_entry_header(*nested_name, nested->is_object() ? 0x03 : 0x04);
+                write_number<std::int32_t>(to_bson_length(nested_sizes[next_size++]), true);
+                parents.push_back(std::move(current));
+                current = bson_frame(nested);
+                continue;
+            }
+
+            oa.write_character(to_char_type(0x00));
+            if (parents.empty())
+            {
+                return;
+            }
+            current = std::move(parents.back());
+            parents.pop_back();
+        }
     }
 
     //////////
diff --git a/tests/src/unit-bson.cpp b/tests/src/unit-bson.cpp
index 669a4bfe1..2cc095a37 100644
--- a/tests/src/unit-bson.cpp
+++ b/tests/src/unit-bson.cpp
@@ -49,7 +49,7 @@ using huge_binary_json = nlohmann::basic_json <
 // for *object keys* (e.g. "s" or "nested" below). Only the designated test
 // value is meant to lie about its size - if every huge_string_t (including
 // keys) reported a huge size, the running totals computed while walking the
-// BSON document (see calc_bson_object_size & friends in binary_writer.hpp)
+// BSON document (see calc_bson_sizes in binary_writer.hpp)
 // would need more than 32 bits, and on platforms where std::size_t is only
 // 32 bits wide that arithmetic would silently wrap around, producing wrong
 // (or even unguarded) lengths. The fake size is therefore opt-in via
@@ -1697,3 +1697,67 @@ TEST_CASE("BSON roundtrips" * doctest::skip())
         }
     }
 }
+
+TEST_CASE("BSON: deeply nested values")
+{
+    SECTION("documents and arrays round-trip at every depth")
+    {
+        // nested documents and arrays, with siblings on every level, so
+        // every length prefix covers entries of both kinds
+        json value = "leaf";
+        for (std::size_t depth = 0; depth <= 300; ++depth)
+        {
+            CAPTURE(depth);
+            const json document = {{"value", value}, {"n", depth}};
+            CHECK(json::from_bson(json::to_bson(document)) == document);
+
+value = depth % 2 == 0 ? json{{"a", std::move(value)}, {"b", {1, "x"}}} :
+            json::array({std::move(value), depth, json::object()});
+        }
+    }
+
+    SECTION("a key containing U+0000 is rejected before anything is written")
+    {
+        json value = json::object({{std::string("bad\0key", 7), 1}});
+        for (std::size_t depth = 0; depth < 200; ++depth)
+        {
+            value = json{{"a", {{"b", 1}}}, {"z", std::move(value)}};
+        }
+        std::vector<std::uint8_t> output;
+        CHECK_THROWS_AS(json::to_bson(value, output), json::out_of_range&);
+        CHECK(output.empty());
+    }
+
+    SECTION("values nested too deeply for the call stack (#5392)")
+    {
+        // serializing recursed once per nesting level, and computed every
+        // nested document's length by walking everything below it again.
+        // The values are only parsed, serialized and walked, never copied or
+        // compared, since those recurse too.
+        const std::size_t depth = 100000;
+        for (const bool objects :
+                {
+                    false, true
+                })
+        {
+            CAPTURE(objects);
+            std::string text = "{\"a\":";
+            for (std::size_t i = 0; i < depth; ++i)
+            {
+                text += objects ? "{\"a\":" : "[";
+            }
+            text += "1";
+            text.append(depth, objects ? '}' : ']');
+            text += "}";
+
+            const auto bson = json::to_bson(json::parse(text));
+            const auto result = json::from_bson(bson);
+            const json* p = &result.at("a");
+            for (std::size_t i = 0; i < depth; ++i)
+            {
+                p = objects ? &p->at("a") : &p->at(0);
+            }
+            CHECK(*p == 1);
+        }
+    }
+}