diff --git a/source/fuzz/fuzzer_pass_add_parameters.cpp b/source/fuzz/fuzzer_pass_add_parameters.cpp
index 9273452..c03b4f4 100644
--- a/source/fuzz/fuzzer_pass_add_parameters.cpp
+++ b/source/fuzz/fuzzer_pass_add_parameters.cpp
@@ -32,7 +32,16 @@
 FuzzerPassAddParameters::~FuzzerPassAddParameters() = default;
 
 void FuzzerPassAddParameters::Apply() {
-  const auto& type_candidates = ComputeTypeCandidates();
+  // Compute type candidates for the new parameter.
+  std::vector<uint32_t> type_candidates;
+  for (const auto& type_inst : GetIRContext()->module()->GetTypes()) {
+    const auto* type =
+        GetIRContext()->get_type_mgr()->GetType(type_inst->result_id());
+    assert(type && "Type instruction is not registered in the type manager");
+    if (TransformationAddParameter::IsParameterTypeSupported(*type)) {
+      type_candidates.push_back(type_inst->result_id());
+    }
+  }
 
   if (type_candidates.empty()) {
     // The module contains no suitable types to use in new parameters.
@@ -71,32 +80,6 @@
   }
 }
 
-std::vector<uint32_t> FuzzerPassAddParameters::ComputeTypeCandidates() const {
-  std::vector<uint32_t> result;
-
-  for (const auto* type_inst : GetIRContext()->module()->GetTypes()) {
-    // TODO(https://github.com/KhronosGroup/SPIRV-Tools/issues/3403):
-    //  the number of types we support here is limited by the number of types
-    //  supported by |FindOrCreateZeroConstant|.
-    switch (type_inst->opcode()) {
-      case SpvOpTypeBool:
-      case SpvOpTypeInt:
-      case SpvOpTypeFloat:
-      case SpvOpTypeArray:
-      case SpvOpTypeMatrix:
-      case SpvOpTypeVector:
-      case SpvOpTypeStruct: {
-        result.push_back(type_inst->result_id());
-      } break;
-      default:
-        // Ignore other types.
-        break;
-    }
-  }
-
-  return result;
-}
-
 uint32_t FuzzerPassAddParameters::GetNumberOfParameters(
     const opt::Function& function) const {
   const auto* type = GetIRContext()->get_type_mgr()->GetType(
diff --git a/source/fuzz/fuzzer_pass_add_parameters.h b/source/fuzz/fuzzer_pass_add_parameters.h
index feb009f..f1261ae 100644
--- a/source/fuzz/fuzzer_pass_add_parameters.h
+++ b/source/fuzz/fuzzer_pass_add_parameters.h
@@ -37,10 +37,6 @@
   void Apply() override;
 
  private:
-  // Uses types, defined in the module, to compute a vector of their ids, which
-  // will be used as type ids of new parameters.
-  std::vector<uint32_t> ComputeTypeCandidates() const;
-
   // Returns number of parameters of |function|.
   uint32_t GetNumberOfParameters(const opt::Function& function) const;
 };
diff --git a/source/fuzz/fuzzer_pass_replace_parameter_with_global.cpp b/source/fuzz/fuzzer_pass_replace_parameter_with_global.cpp
index 87b2b5d..907c5b4 100644
--- a/source/fuzz/fuzzer_pass_replace_parameter_with_global.cpp
+++ b/source/fuzz/fuzzer_pass_replace_parameter_with_global.cpp
@@ -58,7 +58,7 @@
                                param->type_id());
                        assert(param_type && "Parameter has invalid type");
                        return TransformationReplaceParameterWithGlobal::
-                           CanReplaceFunctionParameterType(*param_type);
+                           IsParameterTypeSupported(*param_type);
                      })) {
       continue;
     }
@@ -71,8 +71,9 @@
       param_type =
           GetIRContext()->get_type_mgr()->GetType(replaced_param->type_id());
       assert(param_type && "Parameter has invalid type");
-    } while (!TransformationReplaceParameterWithGlobal::
-                 CanReplaceFunctionParameterType(*param_type));
+    } while (
+        !TransformationReplaceParameterWithGlobal::IsParameterTypeSupported(
+            *param_type));
 
     assert(replaced_param && "Unable to find a parameter to replace");
 
diff --git a/source/fuzz/transformation_add_parameter.cpp b/source/fuzz/transformation_add_parameter.cpp
index b2dd7be..b64c7e5 100644
--- a/source/fuzz/transformation_add_parameter.cpp
+++ b/source/fuzz/transformation_add_parameter.cpp
@@ -56,7 +56,7 @@
   const auto* initializer_type =
       ir_context->get_type_mgr()->GetType(initializer_inst->type_id());
 
-  if (!initializer_type || initializer_type->AsVoid()) {
+  if (!initializer_type || !IsParameterTypeSupported(*initializer_type)) {
     return false;
   }
 
@@ -139,5 +139,28 @@
   return result;
 }
 
+bool TransformationAddParameter::IsParameterTypeSupported(
+    const opt::analysis::Type& type) {
+  // TODO(https://github.com/KhronosGroup/SPIRV-Tools/issues/3403):
+  //  Think about other type instructions we can add here.
+  switch (type.kind()) {
+    case opt::analysis::Type::kBool:
+    case opt::analysis::Type::kInteger:
+    case opt::analysis::Type::kFloat:
+    case opt::analysis::Type::kArray:
+    case opt::analysis::Type::kMatrix:
+    case opt::analysis::Type::kVector:
+      return true;
+    case opt::analysis::Type::kStruct:
+      return std::all_of(type.AsStruct()->element_types().begin(),
+                         type.AsStruct()->element_types().end(),
+                         [](const opt::analysis::Type* element_type) {
+                           return IsParameterTypeSupported(*element_type);
+                         });
+    default:
+      return false;
+  }
+}
+
 }  // namespace fuzz
 }  // namespace spvtools
diff --git a/source/fuzz/transformation_add_parameter.h b/source/fuzz/transformation_add_parameter.h
index 42b5fbb..e6b9019 100644
--- a/source/fuzz/transformation_add_parameter.h
+++ b/source/fuzz/transformation_add_parameter.h
@@ -35,7 +35,8 @@
   // - |function_id| must be a valid result id of some non-entry-point function
   //   in the module.
   // - |initializer_id| must be a valid result id of some instruction in the
-  //   module. Instruction's type may not be OpTypeVoid.
+  //   module. Instruction's type must be supported by this transformation
+  //   as specified by IsParameterTypeSupported function.
   // - |parameter_fresh_id| and |function_type_fresh_id| are fresh ids and are
   //   not equal.
   bool IsApplicable(
@@ -52,6 +53,10 @@
 
   protobufs::Transformation ToMessage() const override;
 
+  // Returns true if the type of the parameter is supported by this
+  // transformation.
+  static bool IsParameterTypeSupported(const opt::analysis::Type& type);
+
  private:
   protobufs::TransformationAddParameter message_;
 };
diff --git a/source/fuzz/transformation_replace_parameter_with_global.cpp b/source/fuzz/transformation_replace_parameter_with_global.cpp
index 2ce7cfe..61c7f10 100644
--- a/source/fuzz/transformation_replace_parameter_with_global.cpp
+++ b/source/fuzz/transformation_replace_parameter_with_global.cpp
@@ -76,7 +76,7 @@
   const auto* param_type =
       ir_context->get_type_mgr()->GetType(param_inst->type_id());
   assert(param_type && "Parameter has invalid type");
-  if (!CanReplaceFunctionParameterType(*param_type)) {
+  if (!IsParameterTypeSupported(*param_type)) {
     return false;
   }
 
@@ -217,7 +217,7 @@
   return result;
 }
 
-bool TransformationReplaceParameterWithGlobal::CanReplaceFunctionParameterType(
+bool TransformationReplaceParameterWithGlobal::IsParameterTypeSupported(
     const opt::analysis::Type& type) {
   // TODO(https://github.com/KhronosGroup/SPIRV-Tools/issues/3403):
   //  Think about other type instructions we can add here.
@@ -230,12 +230,11 @@
     case opt::analysis::Type::kVector:
       return true;
     case opt::analysis::Type::kStruct:
-      return std::all_of(
-          type.AsStruct()->element_types().begin(),
-          type.AsStruct()->element_types().end(),
-          [](const opt::analysis::Type* element_type) {
-            return CanReplaceFunctionParameterType(*element_type);
-          });
+      return std::all_of(type.AsStruct()->element_types().begin(),
+                         type.AsStruct()->element_types().end(),
+                         [](const opt::analysis::Type* element_type) {
+                           return IsParameterTypeSupported(*element_type);
+                         });
     default:
       return false;
   }
diff --git a/source/fuzz/transformation_replace_parameter_with_global.h b/source/fuzz/transformation_replace_parameter_with_global.h
index cd379b0..49e7585 100644
--- a/source/fuzz/transformation_replace_parameter_with_global.h
+++ b/source/fuzz/transformation_replace_parameter_with_global.h
@@ -55,7 +55,7 @@
 
   // Returns true if the type of the parameter is supported by this
   // transformation.
-  static bool CanReplaceFunctionParameterType(const opt::analysis::Type& type);
+  static bool IsParameterTypeSupported(const opt::analysis::Type& type);
 
  private:
   protobufs::TransformationReplaceParameterWithGlobal message_;