diff --git a/toolchain/sem_ir/inst_fingerprinter.cpp b/toolchain/sem_ir/inst_fingerprinter.cpp
index 0d6e78f1ee7e..e57ff41f0a9c 100644
--- a/toolchain/sem_ir/inst_fingerprinter.cpp
+++ b/toolchain/sem_ir/inst_fingerprinter.cpp
@@ -4,6 +4,8 @@
 
 #include "toolchain/sem_ir/inst_fingerprinter.h"
 
+#include <variant>
+
 #include "common/ostream.h"
 #include "llvm/ADT/STLExtras.h"
 #include "llvm/ADT/SmallVector.h"
@@ -19,7 +21,8 @@ struct Worklist {
   // The file containing the instruction we're currently processing.
   const File* sem_ir = nullptr;
   // The instructions we need to compute fingerprints for.
-  llvm::SmallVector<std::pair<const File*, InstId>> todo;
+  llvm::SmallVector<std::pair<const File*, std::variant<InstId, InstBlockId>>>
+      todo;
   // The contents of the current instruction as accumulated so far. This is used
   // to build a Merkle tree containing a fingerprint for the current
   // instruction.
@@ -28,12 +31,6 @@ struct Worklist {
   // the cache if not already present.
   Map<std::pair<const File*, InstId>, uint64_t>* fingerprints;
 
-  // Prepare to fingerprint a new instruction.
-  auto Prepare(const File* file) -> void {
-    sem_ir = file;
-    contents.clear();
-  }
-
   // Finish fingerprinting and compute the fingerprint.
   auto Finish() -> uint64_t { return llvm::stable_hash_combine(contents); }
 
@@ -301,7 +298,39 @@ struct Worklist {
   auto Run() -> uint64_t {
     CARBON_CHECK(!todo.empty());
     while (true) {
-      auto [next_sem_ir, next_inst_id] = todo.back();
+      const size_t init_size = todo.size();
+      auto [next_sem_ir, next_inst_id_or_block] = todo.back();
+
+      sem_ir = next_sem_ir;
+      contents.clear();
+
+      if (auto* inst_block_id =
+              std::get_if<InstBlockId>(&next_inst_id_or_block)) {
+        // Add all the instructions in the block so they all contribute to the
+        // `contents`.
+        Add(*inst_block_id);
+
+        // If we didn't add any more work, then we have a fingerprint for the
+        // instruction block, otherwise we wait until that work is completed. If
+        // the block is the last thing in `todo`, we return the fingerprint.
+        // Otherwise we would just discard it because we don't currently cache
+        // the fingerprint for blocks, but we really only expect `InstBlockId`
+        // to be at the bottom of the `todo` stack since they are not added to
+        // `todo` during Run().
+        if (todo.size() == init_size) {
+          auto fingerprint = Finish();
+          todo.pop_back();
+          CARBON_CHECK(todo.empty(),
+                       "An InstBlockId was inserted into `todo` during Run()");
+          return fingerprint;
+        }
+
+        // Move on to processing the instructions in the block; we will come
+        // back to this branch once they are done.
+        continue;
+      }
+
+      auto next_inst_id = std::get<InstId>(next_inst_id_or_block);
 
       // If we already have a fingerprint for this instruction, we have nothing
       // to do. Just pop it from `todo`.
@@ -317,13 +346,9 @@ struct Worklist {
       // Keep this instruction in `todo` for now. If we add more work, we'll
       // finish that work and process this instruction again, and if not, we'll
       // pop the instruction at the end of the loop.
-      size_t init_size = todo.size();
       auto inst = next_sem_ir->insts().Get(next_inst_id);
       auto [arg0_kind, arg1_kind] = inst.ArgKinds();
 
-      // Prepare to fingerprint this instruction.
-      Prepare(next_sem_ir);
-
       // Add the instruction's fields to the contents.
       Add(inst.kind());
 
@@ -362,17 +387,9 @@ auto InstFingerprinter::GetOrCompute(const File* file, InstId inst_id)
 
 auto InstFingerprinter::GetOrCompute(const File* file,
                                      InstBlockId inst_block_id) -> uint64_t {
-  Worklist worklist = {.todo = {}, .fingerprints = &fingerprints_};
-  worklist.Prepare(file);
-  worklist.Add(inst_block_id);
-  if (!worklist.todo.empty()) {
-    worklist.Run();
-    worklist.Prepare(file);
-    worklist.Add(inst_block_id);
-  }
-  CARBON_CHECK(worklist.todo.empty(),
-               "Should not require more than two passes.");
-  return worklist.Finish();
+  Worklist worklist = {.todo = {{file, inst_block_id}},
+                       .fingerprints = &fingerprints_};
+  return worklist.Run();
 }
 
 }  // namespace Carbon::SemIR