diff --git a/compat/arc4random.c b/compat/arc4random.c
index b536d3143..486ab89c6 100644
--- a/compat/arc4random.c
+++ b/compat/arc4random.c
@@ -57,6 +57,8 @@
 #define BLOCKSZ	64
 #define RSBUFSZ	(16*BLOCKSZ)
 
+#define REKEY_BASE	(1024*1024) /* NB. should be a power of 2 */
+
 /* Marked MAP_INHERIT_ZERO, so zero'd out in fork children. */
 static struct {
 	size_t		rs_have;	/* valid bytes at end of rs_buf */
@@ -179,6 +181,7 @@ static void
 _rs_stir(void)
 {
 	u_char rnd[KEYSZ + IVSZ];
+	uint32_t rekey_fuzz = 0;
 
 	if (getentropy(rnd, sizeof rnd) == -1) {
 		if(errno != ENOSYS ||
@@ -201,7 +204,10 @@ _rs_stir(void)
 	rs->rs_have = 0;
 	memset(rsx->rs_buf, 0, sizeof(rsx->rs_buf));
 
-	rs->rs_count = 1600000;
+	/* rekey interval should not be predictable */
+	chacha_encrypt_bytes(&rsx->rs_chacha, (uint8_t *)&rekey_fuzz,
+	    (uint8_t *)&rekey_fuzz, sizeof(rekey_fuzz));
+	rs->rs_count = REKEY_BASE + (rekey_fuzz % REKEY_BASE);
 }
 
 static inline void