diff --git a/CMakeLists.txt b/CMakeLists.txt
index 54b4c55..c99c66a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,7 +1,7 @@
 cmake_minimum_required(VERSION 3.24)
 
 project(tatami_hdf5
-    VERSION 2.0.1
+    VERSION 2.0.2
     DESCRIPTION "tatami bindings for HDF5"
     LANGUAGES CXX)
 
diff --git a/include/tatami_hdf5/serialize.hpp b/include/tatami_hdf5/serialize.hpp
index b16b485..2dfc019 100644
--- a/include/tatami_hdf5/serialize.hpp
+++ b/include/tatami_hdf5/serialize.hpp
@@ -6,15 +6,15 @@
  * @brief Default locking for serial access.
  */
 
-/**
- * @cond
- */
 #ifndef TATAMI_HDF5_PARALLEL_LOCK
 #include "subpar/subpar.hpp"
 #ifndef SUBPAR_USES_OPENMP
-#include <thread>
 #include <mutex>
+#include <thread>
 namespace tatami_hdf5 {
+// We put this in a separate function instead of a static function variable
+// inside serialize(), as we would get a different mutex for each instance 
+// of serialize() created with a different Function_.
 inline auto& get_default_hdf5_lock() {
     static std::mutex hdf5_lock;
     return hdf5_lock;
@@ -22,9 +22,6 @@ inline auto& get_default_hdf5_lock() {
 }
 #endif
 #endif
-/**
- * @endcond
- */
 
 namespace tatami_hdf5 {
 
@@ -48,15 +45,18 @@ template<class Function_>
 void serialize(Function_ f) {
 #ifdef TATAMI_HDF5_PARALLEL_LOCK
     TATAMI_HDF5_PARALLEL_LOCK(f);
-#elif defined(SUBPAR_USES_OPENMP)
+#else
+#ifdef SUBPAR_USES_OPENMP
     #pragma omp critical(hdf5)
     {
         f();
     }
 #else
-    std::lock_guard<std::mutex> thing(get_hdf5_lock());
+    auto& h5lock = get_default_hdf5_lock();
+    std::lock_guard<std::mutex> thing(h5lock);
     f();
 #endif
+#endif
 }
 
 }
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index dab29ee..3934c30 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -51,6 +51,15 @@ endmacro()
 
 decorate_test(libtest)
 
+add_executable(
+    cuslocktest
+    src/write_compressed_sparse_matrix.cpp
+    src/DenseMatrix.cpp
+    src/CompressedSparseMatrix.cpp
+)
+decorate_test(cuslocktest)
+target_compile_definitions(cuslocktest PRIVATE TATAMI_HDF5_TEST_PARALLEL_ONLY=1 TATAMI_HDF5_TEST_CUSTOM_LOCK=1)
+
 find_package(OpenMP)
 if(OpenMP_FOUND)
     add_executable(
@@ -59,7 +68,6 @@ if(OpenMP_FOUND)
         src/DenseMatrix.cpp
         src/CompressedSparseMatrix.cpp
     )
-
     decorate_test(omptest)
     target_link_libraries(omptest OpenMP::OpenMP_CXX)
     target_compile_definitions(omptest PRIVATE TATAMI_HDF5_TEST_PARALLEL_ONLY=1)
diff --git a/tests/src/custom_parallel.h b/tests/src/custom_parallel.h
index b80ff31..e5e597c 100644
--- a/tests/src/custom_parallel.h
+++ b/tests/src/custom_parallel.h
@@ -6,6 +6,7 @@
 // OpenMP critical regions instead of using this mutex-based lock.
 
 #ifndef _OPENMP
+#ifdef TATAMI_HDF5_TEST_CUSTOM_LOCK
 #include <thread>
 #include <mutex>
 
@@ -24,3 +25,4 @@ void hdf5_serialize(Function f) {
 #endif
 
 #endif
+#endif