diff --git a/source/fuzz/transformation_add_constant_composite.cpp b/source/fuzz/transformation_add_constant_composite.cpp
index c036cd5..ac4d599 100644
--- a/source/fuzz/transformation_add_constant_composite.cpp
+++ b/source/fuzz/transformation_add_constant_composite.cpp
@@ -50,7 +50,8 @@
     return false;
   }
   // Gather up the operands for the composite constant, in the process checking
-  // whether the given type really defines a composite.
+  // whether the given type really defines a composite and - in the case of a
+  // struct - whether its decorations are OK.
   std::vector<uint32_t> constituent_type_ids;
   switch (composite_type_instruction->opcode()) {
     case SpvOpTypeArray:
@@ -72,6 +73,19 @@
       }
       break;
     case SpvOpTypeStruct:
+      // We do not create constants of structs decorated with Block nor
+      // BufferBlock.  The SPIR-V spec does not explicitly disallow this, but it
+      // seems like a strange thing to do, so we disallow it to avoid triggering
+      // low priorty edge case issues related to it.
+      for (auto decoration : {SpvDecorationBlock, SpvDecorationBufferBlock}) {
+        if (!ir_context->get_decoration_mgr()->WhileEachDecoration(
+                composite_type_instruction->result_id(), decoration,
+                [](const opt::Instruction & /*unused*/) -> bool {
+                  return false;
+                })) {
+          return false;
+        }
+      }
       composite_type_instruction->ForEachInOperand(
           [&constituent_type_ids](const uint32_t* member_type_id) {
             constituent_type_ids.push_back(*member_type_id);
diff --git a/source/fuzz/transformation_add_constant_composite.h b/source/fuzz/transformation_add_constant_composite.h
index 51345ca..56ac52a 100644
--- a/source/fuzz/transformation_add_constant_composite.h
+++ b/source/fuzz/transformation_add_constant_composite.h
@@ -38,6 +38,8 @@
   // - |message_.type_id| must be the id of a composite type
   // - |message_.constituent_id| must refer to ids that match the constituent
   //   types of this composite type
+  // - If |message_.type_id| is a struc type, it must not have the Block or
+  //   BufferBlock decoration
   bool IsApplicable(
       opt::IRContext* ir_context,
       const TransformationContext& transformation_context) const override;
diff --git a/test/fuzz/transformation_add_constant_composite_test.cpp b/test/fuzz/transformation_add_constant_composite_test.cpp
index 082b673..2b8b838 100644
--- a/test/fuzz/transformation_add_constant_composite_test.cpp
+++ b/test/fuzz/transformation_add_constant_composite_test.cpp
@@ -195,6 +195,92 @@
   ASSERT_TRUE(IsEqual(env, after_transformation, context.get()));
 }
 
+TEST(TransformationAddConstantCompositeTest, DisallowBufferBlockDecoration) {
+  std::string shader = R"(
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint GLCompute %4 "main"
+               OpExecutionMode %4 LocalSize 1 1 1
+               OpSource ESSL 320
+               OpName %4 "main"
+               OpName %7 "buf"
+               OpMemberName %7 0 "a"
+               OpMemberName %7 1 "b"
+               OpName %9 ""
+               OpMemberDecorate %7 0 Offset 0
+               OpMemberDecorate %7 1 Offset 4
+               OpDecorate %7 BufferBlock
+               OpDecorate %9 DescriptorSet 0
+               OpDecorate %9 Binding 0
+          %2 = OpTypeVoid
+          %3 = OpTypeFunction %2
+          %6 = OpTypeInt 32 1
+         %10 = OpConstant %6 42
+          %7 = OpTypeStruct %6 %6
+          %8 = OpTypePointer Uniform %7
+          %9 = OpVariable %8 Uniform
+          %4 = OpFunction %2 None %3
+          %5 = OpLabel
+               OpReturn
+               OpFunctionEnd
+  )";
+
+  const auto env = SPV_ENV_UNIVERSAL_1_0;
+  const auto consumer = nullptr;
+  const auto context = BuildModule(env, consumer, shader, kFuzzAssembleOption);
+  ASSERT_TRUE(IsValid(env, context.get()));
+
+  spvtools::ValidatorOptions validator_options;
+  TransformationContext transformation_context(
+      MakeUnique<FactManager>(context.get()), validator_options);
+  ASSERT_FALSE(TransformationAddConstantComposite(100, 7, {10, 10}, false)
+                   .IsApplicable(context.get(), transformation_context));
+}
+
+TEST(TransformationAddConstantCompositeTest, DisallowBlockDecoration) {
+  std::string shader = R"(
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint GLCompute %4 "main" %9
+               OpExecutionMode %4 LocalSize 1 1 1
+               OpSource ESSL 320
+               OpName %4 "main"
+               OpName %7 "buf"
+               OpMemberName %7 0 "a"
+               OpMemberName %7 1 "b"
+               OpName %9 ""
+               OpMemberDecorate %7 0 Offset 0
+               OpMemberDecorate %7 1 Offset 4
+               OpDecorate %7 Block
+               OpDecorate %9 DescriptorSet 0
+               OpDecorate %9 Binding 0
+          %2 = OpTypeVoid
+          %3 = OpTypeFunction %2
+          %6 = OpTypeInt 32 1
+         %10 = OpConstant %6 42
+          %7 = OpTypeStruct %6 %6
+          %8 = OpTypePointer StorageBuffer %7
+          %9 = OpVariable %8 StorageBuffer
+          %4 = OpFunction %2 None %3
+          %5 = OpLabel
+               OpReturn
+               OpFunctionEnd
+  )";
+
+  const auto env = SPV_ENV_UNIVERSAL_1_5;
+  const auto consumer = nullptr;
+  const auto context = BuildModule(env, consumer, shader, kFuzzAssembleOption);
+  ASSERT_TRUE(IsValid(env, context.get()));
+
+  spvtools::ValidatorOptions validator_options;
+  TransformationContext transformation_context(
+      MakeUnique<FactManager>(context.get()), validator_options);
+  ASSERT_FALSE(TransformationAddConstantComposite(100, 7, {10, 10}, false)
+                   .IsApplicable(context.get(), transformation_context));
+}
+
 }  // namespace
 }  // namespace fuzz
 }  // namespace spvtools