diff --git a/gio/tests/stream-rw_all.c b/gio/tests/stream-rw_all.c
index 4d9035529..64233df4f 100644
--- a/gio/tests/stream-rw_all.c
+++ b/gio/tests/stream-rw_all.c
@@ -119,10 +119,10 @@ static void
 test_read_all_async_memory (void)
 {
   GInputStream *ms;
-  gchar b[24] = "0123456789ABCDEFGHIJ!@#$";
+  gchar b[] = "0123456789ABCDEFGHIJ!@#$";
   gchar buf[10];
 
-  ms = g_memory_input_stream_new_from_data (b, sizeof b, NULL);
+  ms = g_memory_input_stream_new_from_data (b, strlen (b), NULL);
 
   g_input_stream_read_all_async (ms, buf, 10, 0, NULL, read_done, NULL);
   wait_for_read (TRUE, 10);
diff --git a/gobject/tests/reference.c b/gobject/tests/reference.c
index 0fe655ea0..0408a8edf 100644
--- a/gobject/tests/reference.c
+++ b/gobject/tests/reference.c
@@ -1,5 +1,7 @@
 #include <glib-object.h>
 
+#include "gvalgrind.h"
+
 static void
 test_fundamentals (void)
 {
@@ -952,6 +954,16 @@ test_weak_ref_concurrent (gconstpointer testdata)
   ConcurrentThreadData thread_data[CONCURRENT_N_THREADS];
   GWeakRef weak_ref = { 0 };
 
+  /* The race in this test is very hard to reproduce under valgrind, so skip it.
+   * Otherwise the test can run for tens of minutes. */
+#if defined (ENABLE_VALGRIND)
+  if (RUNNING_ON_VALGRIND)
+    {
+      g_test_skip ("Skipping hard-to-reproduce race under valgrind");
+      return;
+    }
+#endif
+
   /* Let several threads call g_weak_ref_set() & g_weak_ref_get() in a loop. */
 
   for (i = 0; i < CONCURRENT_N_OBJS; i++)