diff --git a/src/ir_opt/constant_propagation_pass.cpp b/src/ir_opt/constant_propagation_pass.cpp
index 17c59fa4..cf7592cc 100644
--- a/src/ir_opt/constant_propagation_pass.cpp
+++ b/src/ir_opt/constant_propagation_pass.cpp
@@ -8,6 +8,7 @@
 
 #include "common/assert.h"
 #include "common/bit_util.h"
+#include "common/safe_ops.h"
 #include "common/common_types.h"
 #include "frontend/ir/basic_block.h"
 #include "frontend/ir/ir_emitter.h"
@@ -254,7 +255,7 @@ void FoldOR(IR::Inst& inst, bool is_32_bit) {
     }
 }
 
-void FoldShifts(IR::Inst& inst) {
+bool FoldShifts(IR::Inst& inst) {
     IR::Inst* carry_inst = inst.GetAssociatedPseudoOperation(Op::GetCarryFromOp);
 
     // The 32-bit variants can contain 3 arguments, while the
@@ -264,14 +265,19 @@ void FoldShifts(IR::Inst& inst) {
     }
 
     const auto shift_amount = inst.GetArg(1);
-    if (!shift_amount.IsZero()) {
-        return;
+    if (shift_amount.IsZero()) {
+        if (carry_inst) {
+            carry_inst->ReplaceUsesWith(inst.GetArg(2));
+        }
+        inst.ReplaceUsesWith(inst.GetArg(0));
+        return false;
     }
 
-    if (carry_inst) {
-        carry_inst->ReplaceUsesWith(inst.GetArg(2));
+    if (!inst.AreAllArgsImmediates() || carry_inst) {
+        return false;
     }
-    inst.ReplaceUsesWith(inst.GetArg(0));
+
+    return true;
 }
 
 void FoldSignExtendXToWord(IR::Inst& inst) {
@@ -332,14 +338,84 @@ void ConstantPropagation(IR::Block& block) {
             FoldMostSignificantBit(inst);
             break;
         case Op::LogicalShiftLeft32:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, true, Safe::LogicalShiftLeft<u32>(inst.GetArg(0).GetU32(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::LogicalShiftLeft64:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, false, Safe::LogicalShiftLeft<u64>(inst.GetArg(0).GetU64(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::LogicalShiftRight32:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, true, Safe::LogicalShiftRight<u32>(inst.GetArg(0).GetU32(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::LogicalShiftRight64:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, false, Safe::LogicalShiftRight<u64>(inst.GetArg(0).GetU64(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::ArithmeticShiftRight32:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, true, Safe::ArithmeticShiftRight<u32>(inst.GetArg(0).GetU32(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::ArithmeticShiftRight64:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, false, Safe::ArithmeticShiftRight<u64>(inst.GetArg(0).GetU64(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::RotateRight32:
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, true, Common::RotateRight<u32>(inst.GetArg(0).GetU32(), inst.GetArg(1).GetU8()));
+            }
+            break;
         case Op::RotateRight64:
-            FoldShifts(inst);
+            if (FoldShifts(inst)) {
+                ReplaceUsesWith(inst, false, Common::RotateRight<u64>(inst.GetArg(0).GetU64(), inst.GetArg(1).GetU8()));
+            }
+            break;
+        case Op::LogicalShiftLeftMasked32:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, true, inst.GetArg(0).GetU32() << (inst.GetArg(1).GetU32() & 0x1f));
+            }
+            break;
+        case Op::LogicalShiftLeftMasked64:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, false, inst.GetArg(0).GetU64() << (inst.GetArg(1).GetU64() & 0x3f));
+            }
+            break;
+        case Op::LogicalShiftRightMasked32:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, true, inst.GetArg(0).GetU32() >> (inst.GetArg(1).GetU32() & 0x1f));
+            }
+            break;
+        case Op::LogicalShiftRightMasked64:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, false, inst.GetArg(0).GetU64() >> (inst.GetArg(1).GetU64() & 0x3f));
+            }
+            break;
+        case Op::ArithmeticShiftRightMasked32:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, true, static_cast<s32>(inst.GetArg(0).GetU32()) >> (inst.GetArg(1).GetU32() & 0x1f));
+            }
+            break;
+        case Op::ArithmeticShiftRightMasked64:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, false, static_cast<s64>(inst.GetArg(0).GetU64()) >> (inst.GetArg(1).GetU64() & 0x3f));
+            }
+            break;
+        case Op::RotateRightMasked32:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, true, Common::RotateRight<u32>(inst.GetArg(0).GetU32(), inst.GetArg(1).GetU32()));
+            }
+            break;
+        case Op::RotateRightMasked64:
+            if (inst.AreAllArgsImmediates()) {
+                ReplaceUsesWith(inst, false, Common::RotateRight<u64>(inst.GetArg(0).GetU64(), inst.GetArg(1).GetU64()));
+            }
             break;
         case Op::Mul32:
         case Op::Mul64: