diff --git a/arc4random.c b/arc4random.c
index c36e3c11b0..b5f66b4c6f 100644
--- a/arc4random.c
+++ b/arc4random.c
@@ -75,8 +75,7 @@
 /* Add platform entropy 32 bytes (256 bits) at a time. */
 #define ADD_ENTROPY 32
 
-/* Re-seed from the platform RNG after generating this many bytes. */
-#define BYTES_BEFORE_RESEED 1600000
+#define REKEY_BASE (1024*1024) /* NB. should be a power of 2 */
 
 struct arc4_stream {
 	unsigned char i;
@@ -343,10 +342,13 @@ arc4_seed(void)
 	return ok ? 0 : -1;
 }
 
+static inline unsigned int
+arc4_getword(void);
 static int
 arc4_stir(void)
 {
 	int     i;
+	ARC4RANDOM_UINT32 rekey_fuzz; 
 
 	if (!rs_initialized) {
 		arc4_init();
@@ -377,7 +379,9 @@ arc4_stir(void)
 	for (i = 0; i < 12*256; i++)
 		(void)arc4_getbyte();
 
-	arc4_count = BYTES_BEFORE_RESEED;
+	rekey_fuzz = arc4_getword();
+	/* rekey interval should not be predictable */
+	arc4_count = REKEY_BASE + (rekey_fuzz % REKEY_BASE);
 
 	return 0;
 }