diff --git a/src/cairo-skiplist-private.h b/src/cairo-skiplist-private.h
index cf1a99bad..3a948afce 100644
--- a/src/cairo-skiplist-private.h
+++ b/src/cairo-skiplist-private.h
@@ -32,6 +32,9 @@
  *   http://citeseer.ist.psu.edu/pugh90skip.html
  */
 
+/* Note that random_level() called from alloc_node_for_level() depends on
+ * this being not more than 16.
+ */
 #define MAX_LEVEL   15
 
 /* Returns the index of the free-list to use for a node at level 'level' */
diff --git a/src/cairo-skiplist.c b/src/cairo-skiplist.c
index 52d846527..2d2fbb002 100644
--- a/src/cairo-skiplist.c
+++ b/src/cairo-skiplist.c
@@ -269,9 +269,12 @@ _cairo_skip_list_fini (cairo_skip_list_t *list)
 static int
 random_level (void)
 {
-    /* tricky bit -- each bit is '1' 75% of the time */
-    long int	bits = lfsr_random() | lfsr_random();
     int	level = 0;
+    /* tricky bit -- each bit is '1' 75% of the time.
+     * This works because we only use the lower MAX_LEVEL
+     * bits, and MAX_LEVEL < 16 */
+    long int	bits = lfsr_random();
+    bits |= bits >> 16;
 
     while (++level < MAX_LEVEL)
     {