diff --git a/src/H5.c b/src/H5.c
index 4d65c0c9771..84eaa5aaca4 100644
--- a/src/H5.c
+++ b/src/H5.c
@@ -215,7 +215,7 @@ H5_init_library(void)
          * executed in LIFO order (i.e., last).
          */
         (void)atexit(H5TS_term_package);
-#endif /* H5_HAVE_THREADSAFE && H5_HAVE_WIN_THREADS */
+#endif /* H5_HAVE_THREADSAFE */
 
         /* Normal library termination code */
         (void)atexit(H5_term_library);
diff --git a/src/H5TSprivate.h b/src/H5TSprivate.h
index 437e70a998b..d15fa92e80e 100644
--- a/src/H5TSprivate.h
+++ b/src/H5TSprivate.h
@@ -63,7 +63,7 @@
 #define H5TS_thread_equal(t1, t2) (GetThreadId(t1) == GetThreadId(t2))
 #else
 #define H5TS_thread_self()        pthread_self()
-#define H5TS_thread_equal(t1, t2) pthread_equal(t1, t2)
+#define H5TS_thread_equal(t1, t2) pthread_equal((t1), (t2))
 #endif
 
 /****************************/
@@ -92,21 +92,16 @@ typedef pthread_once_t  H5TS_once_t;
 typedef void (*H5TS_once_init_func_t)(void);
 #endif
 
-    /*****************************/
-    /* Library-private Variables */
-    /*****************************/
+/*****************************/
+/* Library-private Variables */
+/*****************************/
 
-    /***************************************/
-    /* Library-private Function Prototypes */
-    /***************************************/
+/***************************************/
+/* Library-private Function Prototypes */
+/***************************************/
 
-    /* Library/thread init/term operations */
-    H5_DLL void
-    H5TS_term_package(void);
-#ifdef H5_HAVE_WIN_THREADS
-H5_DLL herr_t H5TS_win32_thread_enter(void);
-H5_DLL herr_t H5TS_win32_thread_exit(void);
-#endif /* H5_HAVE_WIN_THREADS */
+/* Library/thread init/term operations */
+H5_DLL void H5TS_term_package(void);
 
 /* API locking */
 H5_DLL herr_t H5TS_api_lock(void);
diff --git a/src/H5TSwin.c b/src/H5TSwin.c
index 4ce2ddd764e..95d73f788ea 100644
--- a/src/H5TSwin.c
+++ b/src/H5TSwin.c
@@ -47,6 +47,10 @@
 /********************/
 /* Local Prototypes */
 /********************/
+#if defined(H5_BUILT_AS_DYNAMIC_LIB) && defined(H5_HAVE_WIN32_API)
+static herr_t H5TS__win32_thread_enter(void);
+static herr_t H5TS__win32_thread_exit(void);
+#endif
 
 /*********************/
 /* Package Variables */
@@ -94,8 +98,9 @@ H5TS__win32_process_enter(PINIT_ONCE InitOnce, PVOID Parameter, PVOID *lpContex)
     FUNC_LEAVE_NOAPI_NAMECHECK_ONLY(ret_value)
 } /* H5TS__win32_process_enter() */
 
+#if defined(H5_BUILT_AS_DYNAMIC_LIB) && defined(H5_HAVE_WIN32_API)
 /*--------------------------------------------------------------------------
- * Function:    H5TS_win32_thread_enter
+ * Function:    H5TS__win32_thread_enter
  *
  * Purpose:     Per-thread setup on Windows when using Win32 threads.
  *
@@ -103,21 +108,24 @@ H5TS__win32_process_enter(PINIT_ONCE InitOnce, PVOID Parameter, PVOID *lpContex)
  *
  *--------------------------------------------------------------------------
  */
-herr_t
-H5TS_win32_thread_enter(void){FUNC_ENTER_NOAPI_NAMECHECK_ONLY
+static herr_t
+H5TS__win32_thread_enter(void)
+{
+    FUNC_ENTER_NOAPI_NAMECHECK_ONLY
 
-                                  /* Currently a placeholder function.  TLS setup is performed
-                                   * elsewhere in the library.
-                                   *
-                                   * WARNING: Do NOT use C standard library functions here.
-                                   * CRT functions are not allowed in DllMain, which is where this code
-                                   * is used.
-                                   */
+    /* Currently a placeholder function.  TLS setup is performed
+     * elsewhere in the library.
+     *
+     * WARNING: Do NOT use C standard library functions here.
+     * CRT functions are not allowed in DllMain, which is where this code
+     * is used.
+     */
 
-                                  FUNC_LEAVE_NOAPI_NAMECHECK_ONLY(SUCCEED)} /* H5TS_win32_thread_enter() */
+    FUNC_LEAVE_NOAPI_NAMECHECK_ONLY(SUCCEED)
+} /* H5TS__win32_thread_enter() */
 
 /*--------------------------------------------------------------------------
- * Function:    H5TS_win32_thread_exit
+ * Function:    H5TS__win32_thread_exit
  *
  * Purpose:     Per-thread cleanup on Windows when using Win32 threads.
  *
@@ -125,7 +133,8 @@ H5TS_win32_thread_enter(void){FUNC_ENTER_NOAPI_NAMECHECK_ONLY
  *
  *--------------------------------------------------------------------------
  */
-herr_t H5TS_win32_thread_exit(void)
+static herr_t
+H5TS__win32_thread_exit(void)
 {
     herr_t ret_value = SUCCEED;
 
@@ -151,9 +160,8 @@ herr_t H5TS_win32_thread_exit(void)
 
 done:
     FUNC_LEAVE_NOAPI_NAMECHECK_ONLY(ret_value)
-} /* H5TS_win32_thread_exit() */
+} /* H5TS__win32_thread_exit() */
 
-#if defined(H5_BUILT_AS_DYNAMIC_LIB) && defined(H5_HAVE_WIN32_API)
 /*-------------------------------------------------------------------------
  * Function:    DllMain
  *
@@ -189,12 +197,12 @@ DllMain(_In_ HINSTANCE hinstDLL, _In_ DWORD fdwReason, _In_ LPVOID lpvReserved)
             break;
 
         case DLL_THREAD_ATTACH:
-            if (H5TS_win32_thread_enter() < 0)
+            if (H5TS__win32_thread_enter() < 0)
                 fOkay = false;
             break;
 
         case DLL_THREAD_DETACH:
-            if (H5TS_win32_thread_exit() < 0)
+            if (H5TS__win32_thread_exit() < 0)
                 fOkay = false;
             break;