diff --git a/Misc/valgrind-python.supp b/Misc/valgrind-python.supp
index a08eaac..e50fc4b 100644
--- a/Misc/valgrind-python.supp
+++ b/Misc/valgrind-python.supp
@@ -47,6 +47,39 @@
 #
 
 {
+   Suppress leaking the GIL.  Happens once per process, see comment in ceval.c.
+   Memcheck:Leak
+   fun:malloc
+   fun:PyThread_allocate_lock
+   fun:PyEval_InitThreads
+}
+
+{
+   Suppress leaking the GIL after a fork.
+   Memcheck:Leak
+   fun:malloc
+   fun:PyThread_allocate_lock
+   fun:PyEval_ReInitThreads
+}
+
+{
+   Suppress leaking the autoTLSkey.  This looks like it shouldn't leak though.
+   Memcheck:Leak
+   fun:malloc
+   fun:PyThread_create_key
+   fun:_PyGILState_Init
+   fun:Py_InitializeEx
+   fun:Py_Main
+}
+
+{
+   Hmmm, is this a real leak or like the GIL?
+   Memcheck:Leak
+   fun:malloc
+   fun:PyThread_ReInitTLS
+}
+
+{
    Handle PyMalloc confusing valgrind (possibly leaked)
    Memcheck:Leak
    fun:realloc