diff --git a/core/prelude/operators.carbon b/core/prelude/operators.carbon
index 7854c9768716..e4fe994ec49a 100644
--- a/core/prelude/operators.carbon
+++ b/core/prelude/operators.carbon
@@ -4,101 +4,7 @@
 
 package Core library "prelude/operators" api;
 
-interface Add {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface AddAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface BitAnd {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface BitAndAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface BitComplement {
-  fn Op[self: Self]() -> Self;
-}
-
-interface BitOr {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface BitOrAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface BitXor {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface BitXorAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Dec {
-  fn Op[addr self: Self*]();
-}
-
-interface Div {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface DivAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Eq {
-  fn Equal[self: Self](other: Self) -> bool;
-  fn NotEqual[self: Self](other: Self) -> bool;
-}
-
-interface Inc {
-  fn Op[addr self: Self*]();
-}
-
-interface LeftShift {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface LeftShiftAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Mod {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface ModAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Mul {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface MulAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Negate {
-  fn Op[self: Self]() -> Self;
-}
-
-interface Ordered {
-  // TODO: fn Compare
-  fn Less[self: Self](other: Self) -> bool;
-  fn LessOrEquivalent[self: Self](other: Self) -> bool;
-  fn Greater[self: Self](other: Self) -> bool;
-  fn GreaterOrEquivalent[self: Self](other: Self) -> bool;
-}
-
-interface RightShift {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface RightShiftAssign {
-  fn Op[addr self: Self*](other: Self);
-}
-
-interface Sub {
-  fn Op[self: Self](other: Self) -> Self;
-}
-interface SubAssign {
-  fn Op[addr self: Self*](other: Self);
-}
+// TODO: Add a mechanism to re-export the names declared here.
+import library "prelude/operators/arithmetic";
+import library "prelude/operators/bitwise";
+import library "prelude/operators/comparison";
diff --git a/core/prelude/operators/arithmetic.carbon b/core/prelude/operators/arithmetic.carbon
new file mode 100644
index 000000000000..0113229bb68d
--- /dev/null
+++ b/core/prelude/operators/arithmetic.carbon
@@ -0,0 +1,70 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+package Core library "prelude/operators/arithmetic" api;
+
+// Addition: `a + b`.
+interface Add {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Addition with assignment: `a += b`.
+interface AddAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Increment: `++a`.
+interface Inc {
+  fn Op[addr self: Self*]();
+}
+
+// Negation: `-a`.
+interface Negate {
+  fn Op[self: Self]() -> Self;
+}
+
+// Subtraction: `a - b`.
+interface Sub {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Subtraction with assignment: `a -= b`.
+interface SubAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Decrement: `--a`.
+interface Dec {
+  fn Op[addr self: Self*]();
+}
+
+// Multiplication: `a * b`.
+interface Mul {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Multiplication with assignment: `a *= b`.
+interface MulAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Division: `a / b`.
+interface Div {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Division with assignment: `a /= b`.
+interface DivAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Modulo: `a % b`.
+interface Mod {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Modulo with assignment: `a %= b`.
+interface ModAssign {
+  fn Op[addr self: Self*](other: Self);
+}
diff --git a/core/prelude/operators/bitwise.carbon b/core/prelude/operators/bitwise.carbon
new file mode 100644
index 000000000000..7f6c4a7177f2
--- /dev/null
+++ b/core/prelude/operators/bitwise.carbon
@@ -0,0 +1,60 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+package Core library "prelude/operators/bitwise" api;
+
+// Bit complement: `^a`.
+interface BitComplement {
+  fn Op[self: Self]() -> Self;
+}
+
+// Bitwise AND: `a & b`.
+interface BitAnd {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Bitwise AND with assignment: `a &= b`.
+interface BitAndAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Bitwise OR: `a | b`.
+interface BitOr {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Bitwise OR with assignment: `a |= b`.
+interface BitOrAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Bitwise XOR: `a ^ b`.
+interface BitXor {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Bitwise XOR with assignment: `a ^= b`.
+interface BitXorAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Left shift: `a << b`.
+interface LeftShift {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Left shift with assignment: `a <<= b`.
+interface LeftShiftAssign {
+  fn Op[addr self: Self*](other: Self);
+}
+
+// Right shift: `a >> b`.
+interface RightShift {
+  fn Op[self: Self](other: Self) -> Self;
+}
+
+// Right shift with assignment: `a >>= b`.
+interface RightShiftAssign {
+  fn Op[addr self: Self*](other: Self);
+}
diff --git a/core/prelude/operators/comparison.carbon b/core/prelude/operators/comparison.carbon
new file mode 100644
index 000000000000..11bdc65426aa
--- /dev/null
+++ b/core/prelude/operators/comparison.carbon
@@ -0,0 +1,20 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+package Core library "prelude/operators/comparison" api;
+
+// Equality comparison: `a == b` and `a != b`.
+interface Eq {
+  fn Equal[self: Self](other: Self) -> bool;
+  fn NotEqual[self: Self](other: Self) -> bool;
+}
+
+// Relational comparison: `a < b`, `a <= b`, `a > b`, `a >= b`.
+interface Ordered {
+  // TODO: fn Compare
+  fn Less[self: Self](other: Self) -> bool;
+  fn LessOrEquivalent[self: Self](other: Self) -> bool;
+  fn Greater[self: Self](other: Self) -> bool;
+  fn GreaterOrEquivalent[self: Self](other: Self) -> bool;
+}
diff --git a/core/prelude/i32.carbon b/core/prelude/types/i32.carbon
similarity index 69%
rename from core/prelude/i32.carbon
rename to core/prelude/types/i32.carbon
index 365e5e310131..6256563c4ca4 100644
--- a/core/prelude/i32.carbon
+++ b/core/prelude/types/i32.carbon
@@ -2,21 +2,29 @@
 // Exceptions. See /LICENSE for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
-package Core library "i32" api;
+package Core library "prelude/types/i32" api;
 
 import library "prelude/operators";
 
+// TODO: Remove these once prelude/operators re-exports their contents.
+import library "prelude/operators/arithmetic";
+import library "prelude/operators/bitwise";
+import library "prelude/operators/comparison";
+
 impl i32 as Add {
   fn Op[self: Self](other: Self) -> Self = "int.add";
 }
 impl i32 as AddAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self + other;
+    // TODO: Once operator lookup works inside Core.
+    // *self = *self + other;
+    *self = self->(Add.Op)(other);
   }
 }
 impl i32 as Inc {
   fn Op[addr self: Self*]() {
-    *self += 1;
+    // *self += 1;
+    self->(AddAssign.Op)(1);
   }
 }
 
@@ -25,7 +33,8 @@ impl i32 as BitAnd {
 }
 impl i32 as BitAndAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self & other;
+    // *self = *self & other;
+    *self = self->(BitAnd.Op)(other);
   }
 }
 
@@ -38,7 +47,8 @@ impl i32 as BitOr {
 }
 impl i32 as BitOrAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self | other;
+    // *self = *self | other;
+    *self = self->(BitOr.Op)(other);
   }
 }
 
@@ -47,7 +57,8 @@ impl i32 as BitXor {
 }
 impl i32 as BitXorAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self ^ other;
+    // *self = *self ^ other;
+    *self = self->(BitXor.Op)(other);
   }
 }
 
@@ -56,7 +67,8 @@ impl i32 as Div {
 }
 impl i32 as DivAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self / other;
+    // *self = *self / other;
+    *self = self->(Div.Op)(other);
   }
 }
 
@@ -70,7 +82,8 @@ impl i32 as LeftShift {
 }
 impl i32 as LeftShiftAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self << other;
+    // *self = *self << other;
+    *self = self->(LeftShift.Op)(other);
   }
 }
 
@@ -79,7 +92,8 @@ impl i32 as Mod {
 }
 impl i32 as ModAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self % other;
+    // *self = *self % other;
+    *self = self->(Mod.Op)(other);
   }
 }
 
@@ -88,7 +102,8 @@ impl i32 as Mul {
 }
 impl i32 as MulAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self * other;
+    // *self = *self * other;
+    *self = self->(Mul.Op)(other);
   }
 }
 
@@ -109,7 +124,8 @@ impl i32 as RightShift {
 }
 impl i32 as RightShiftAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self >> other;
+    // *self = *self >> other;
+    *self = self->(RightShift.Op)(other);
   }
 }
 
@@ -118,11 +134,13 @@ impl i32 as Sub {
 }
 impl i32 as SubAssign {
   fn Op[addr self: Self*](other: Self) {
-    *self = *self - other;
+    // *self = *self - other;
+    *self = self->(Sub.Op)(other);
   }
 }
 impl i32 as Dec {
   fn Op[addr self: Self*]() {
-    *self -= 1;
+    // *self -= 1;
+    self->(SubAssign.Op)(1);
   }
 }
diff --git a/examples/sieve.carbon b/examples/sieve.carbon
index 921961f22daa..21fc616dde3c 100644
--- a/examples/sieve.carbon
+++ b/examples/sieve.carbon
@@ -4,11 +4,12 @@
 
 // Compute and return the number of primes less than 1000.
 
-import Core library "operators";
+import Core library "prelude/operators/arithmetic";
+import Core library "prelude/operators/comparison";
 
-// TODO: Copied from i32.carbon.
+// TODO: Copied from core/prelude/types/i32.carbon.
 // Remove the following, once we do cross-file impl lookup.
-// import Core library "i32";
+// import Core library "prelude/types/i32";
 
 impl i32 as Core.Add {
   fn Op[self: Self](other: Self) -> Self = "int.add";
@@ -24,37 +25,6 @@ impl i32 as Core.Inc {
   }
 }
 
-impl i32 as Core.BitAnd {
-  fn Op[self: Self](other: Self) -> Self = "int.and";
-}
-impl i32 as Core.BitAndAssign {
-  fn Op[addr self: Self*](other: Self) {
-    *self = *self & other;
-  }
-}
-
-impl i32 as Core.BitComplement {
-  fn Op[self: Self]() -> Self = "int.complement";
-}
-
-impl i32 as Core.BitOr {
-  fn Op[self: Self](other: Self) -> Self = "int.or";
-}
-impl i32 as Core.BitOrAssign {
-  fn Op[addr self: Self*](other: Self) {
-    *self = *self | other;
-  }
-}
-
-impl i32 as Core.BitXor {
-  fn Op[self: Self](other: Self) -> Self = "int.xor";
-}
-impl i32 as Core.BitXorAssign {
-  fn Op[addr self: Self*](other: Self) {
-    *self = *self ^ other;
-  }
-}
-
 impl i32 as Core.Div {
   fn Op[self: Self](other: Self) -> Self = "int.div";
 }
@@ -69,15 +39,6 @@ impl i32 as Core.Eq {
   fn NotEqual[self: Self](other: Self) -> bool = "int.neq";
 }
 
-impl i32 as Core.LeftShift {
-  fn Op[self: Self](other: Self) -> Self = "int.left_shift";
-}
-impl i32 as Core.LeftShiftAssign {
-  fn Op[addr self: Self*](other: Self) {
-    *self = *self << other;
-  }
-}
-
 impl i32 as Core.Mod {
   fn Op[self: Self](other: Self) -> Self = "int.mod";
 }
@@ -108,15 +69,6 @@ impl i32 as Core.Ordered {
   fn GreaterOrEquivalent[self: Self](other: Self) -> bool = "int.greater_eq";
 }
 
-impl i32 as Core.RightShift {
-  fn Op[self: Self](other: Self) -> Self = "int.right_shift";
-}
-impl i32 as Core.RightShiftAssign {
-  fn Op[addr self: Self*](other: Self) {
-    *self = *self >> other;
-  }
-}
-
 impl i32 as Core.Sub {
   fn Op[self: Self](other: Self) -> Self = "int.sub";
 }