diff --git a/bufferevent-internal.h b/bufferevent-internal.h
index 400c6d96..461c46e7 100644
--- a/bufferevent-internal.h
+++ b/bufferevent-internal.h
@@ -104,6 +104,10 @@ struct bufferevent_rate_limit_group {
 	/** Timeout event that goes off once a tick, when the bucket is ready
 	 * to refill. */
 	struct event master_refill_event;
+
+	/** Seed for weak random number generator. Protected by 'lock' */
+	struct evutil_weakrand_state weakrand_seed;
+
 	/** Lock to protect the members of this group.  This lock should nest
 	 * within every bufferevent lock: if you are holding this lock, do
 	 * not assume you can lock another bufferevent. */
diff --git a/bufferevent_ratelim.c b/bufferevent_ratelim.c
index 02c50228..f7de86a9 100644
--- a/bufferevent_ratelim.c
+++ b/bufferevent_ratelim.c
@@ -438,7 +438,10 @@ bev_refill_callback_(evutil_socket_t fd, short what, void *arg)
 	BEV_UNLOCK(&bev->bev);
 }
 
-/** Helper: grab a random element from a bufferevent group. */
+/** Helper: grab a random element from a bufferevent group.
+ *
+ * Requires that we hold the lock on the group.
+ */
 static struct bufferevent_private *
 bev_group_random_element_(struct bufferevent_rate_limit_group *group)
 {
@@ -452,7 +455,7 @@ bev_group_random_element_(struct bufferevent_rate_limit_group *group)
 
 	EVUTIL_ASSERT(! LIST_EMPTY(&group->members));
 
-	which = evutil_weakrand_() % group->n_members;
+	which = evutil_weakrand_range_(&group->weakrand_seed, group->n_members);
 
 	bev = LIST_FIRST(&group->members);
 	while (which--)
@@ -660,6 +663,9 @@ bufferevent_rate_limit_group_new(struct event_base *base,
 
 	bufferevent_rate_limit_group_set_min_share(g, 64);
 
+	evutil_weakrand_seed_(&g->weakrand_seed,
+	    (ev_uint32_t) ((now.tv_sec + now.tv_usec) + (ev_intptr_t)g));
+
 	return g;
 }
 
diff --git a/event-internal.h b/event-internal.h
index f840058d..78b3fe63 100644
--- a/event-internal.h
+++ b/event-internal.h
@@ -290,6 +290,10 @@ struct event_base {
 	struct event th_notify;
 	/** A function used to wake up the main thread from another thread. */
 	int (*th_notify_fn)(struct event_base *base);
+
+	/** Saved seed for weak random number generator. Some backends use
+	 * this to produce fairness among sockets. Protected by th_base_lock. */
+	struct evutil_weakrand_state weakrand_seed;
 };
 
 struct event_config_entry {
diff --git a/evutil.c b/evutil.c
index abe15604..9307d259 100644
--- a/evutil.c
+++ b/evutil.c
@@ -2273,14 +2273,52 @@ evutil_getenv_(const char *varname)
 	return getenv(varname);
 }
 
-long
-evutil_weakrand_(void)
+ev_uint32_t
+evutil_weakrand_seed_(struct evutil_weakrand_state *state, ev_uint32_t seed)
 {
+	if (seed == 0) {
+		struct timeval tv;
+		evutil_gettimeofday(&tv, NULL);
+		seed = (ev_uint32_t)tv.tv_sec + (ev_uint32_t)tv.tv_usec;
 #ifdef _WIN32
-	return rand();
+		seed += (ev_uint32_t) _getpid();
 #else
-	return random();
+		seed += (ev_uint32_t) getpid();
 #endif
+	}
+	state->seed = seed;
+	return seed;
+}
+
+ev_int32_t
+evutil_weakrand_(struct evutil_weakrand_state *state)
+{
+	/* This RNG implementation is a linear congruential generator, with
+	 * modulus 2^31, multiplier 1103515245, and addend 12345.  It's also
+	 * used by OpenBSD, and by Glibc's TYPE_0 RNG.
+	 *
+	 * The linear congruential generator is not an industrial-strength
+	 * RNG!  It's fast, but it can have higher-order patterns.  Notably,
+	 * the low bits tend to have periodicity.
+	 */
+	state->seed = ((state->seed) * 1103515245 + 12345) & 0x7fffffff;
+	return (ev_int32_t)(state->seed);
+}
+
+ev_int32_t
+evutil_weakrand_range_(struct evutil_weakrand_state *state, ev_int32_t top)
+{
+	ev_int32_t divisor, result;
+
+	/* We can't just do weakrand() % top, since the low bits of the LCG
+	 * are less random than the high ones.  (Specifically, since the LCG
+	 * modulus is 2^N, every 2^m for m<N will divide the modulus, and so
+	 * therefore the low m bits of the LCG will have period 2^m.) */
+	divisor = EVUTIL_WEAKRAND_MAX / top;
+	do {
+		result = evutil_weakrand_(state) / divisor;
+	} while (result >= top);
+	return result;
 }
 
 int
diff --git a/poll.c b/poll.c
index 744c7141..01144854 100644
--- a/poll.c
+++ b/poll.c
@@ -93,6 +93,8 @@ poll_init(struct event_base *base)
 
 	evsig_init_(base);
 
+	evutil_weakrand_seed_(&base->weakrand_seed, 0);
+
 	return (pollop);
 }
 
@@ -183,7 +185,7 @@ poll_dispatch(struct event_base *base, struct timeval *tv)
 	if (res == 0 || nfds == 0)
 		return (0);
 
-	i = random() % nfds;
+	i = evutil_weakrand_range_(&base->weakrand_seed, nfds);
 	for (j = 0; j < nfds; j++) {
 		int what;
 		if (++i == nfds)
diff --git a/select.c b/select.c
index e1d4987c..8ae53cc1 100644
--- a/select.c
+++ b/select.c
@@ -121,6 +121,8 @@ select_init(struct event_base *base)
 
 	evsig_init_(base);
 
+	evutil_weakrand_seed_(&base->weakrand_seed, 0);
+
 	return (sop);
 }
 
@@ -186,7 +188,7 @@ select_dispatch(struct event_base *base, struct timeval *tv)
 	event_debug(("%s: select reports %d", __func__, res));
 
 	check_selectop(sop);
-	i = random() % nfds;
+	i = evutil_weakrand_range_(&base->weakrand_seed, nfds);
 	for (j = 0; j < nfds; ++j) {
 		if (++i >= nfds)
 			i = 0;
diff --git a/test/regress_buffer.c b/test/regress_buffer.c
index dfb680b5..d183b4f9 100644
--- a/test/regress_buffer.c
+++ b/test/regress_buffer.c
@@ -699,6 +699,7 @@ test_evbuffer_add_file(void *ptr)
 	struct event *rev=NULL, *wev=NULL;
 	struct event_base *base = testdata->base;
 	evutil_socket_t pair[2] = {-1, -1};
+	struct evutil_weakrand_state seed = { 123456789U };
 
 	/* This test is highly parameterized based on substrings of its
 	 * argument.  The strings are: */
@@ -757,7 +758,7 @@ test_evbuffer_add_file(void *ptr)
 		data = malloc(1024*512);
 		tt_assert(data);
 		for (i = 0; i < datalen; ++i)
-			data[i] = (char)evutil_weakrand_();
+			data[i] = (char)evutil_weakrand_(&seed);
 	} else {
 		data = strdup("here is a relatively small string.");
 		tt_assert(data);
diff --git a/test/regress_util.c b/test/regress_util.c
index e7662e0f..6aaeeacf 100644
--- a/test/regress_util.c
+++ b/test/regress_util.c
@@ -829,6 +829,7 @@ test_evutil_rand(void *arg)
 	char buf2[32];
 	int counts[256];
 	int i, j, k, n=0;
+	struct evutil_weakrand_state seed = { 12346789U };
 
 	memset(buf2, 0, sizeof(buf2));
 	memset(counts, 0, sizeof(counts));
@@ -836,8 +837,8 @@ test_evutil_rand(void *arg)
 	for (k=0;k<32;++k) {
 		/* Try a few different start and end points; try to catch
 		 * the various misaligned cases of arc4random_buf */
-		int startpoint = evutil_weakrand_() % 4;
-		int endpoint = 32 - (evutil_weakrand_() % 4);
+		int startpoint = evutil_weakrand_(&seed) % 4;
+		int endpoint = 32 - (evutil_weakrand_(&seed) % 4);
 
 		memset(buf2, 0, sizeof(buf2));
 
@@ -868,6 +869,13 @@ test_evutil_rand(void *arg)
 		}
 	}
 
+	evutil_weakrand_seed_(&seed, 0);
+	for (i = 0; i < 10000; ++i) {
+		ev_int32_t r = evutil_weakrand_range_(&seed, 9999);
+		tt_int_op(0, <=, r);
+		tt_int_op(r, <, 9999);
+	}
+
 	/* for (i=0;i<256;++i) { printf("%3d %2d\n", i, counts[i]); } */
 end:
 	;
diff --git a/util-internal.h b/util-internal.h
index 508eae92..5248ab21 100644
--- a/util-internal.h
+++ b/util-internal.h
@@ -254,7 +254,33 @@ int evutil_resolve_(int family, const char *hostname, struct sockaddr *sa,
 
 const char *evutil_getenv_(const char *name);
 
-long evutil_weakrand_(void);
+/* Structure to hold the state of our weak random number generator.
+ */
+struct evutil_weakrand_state {
+	ev_uint32_t seed;
+};
+
+#define EVUTIL_WEAKRAND_MAX EV_INT32_MAX
+
+/* Initialize the state of a week random number generator based on 'seed'.  If
+ * the seed is 0, construct a new seed based on not-very-strong platform
+ * entropy, like the PID and the time of day.
+ *
+ * This function, and the other evutil_weakrand* functions, are meant for
+ * speed, not security or statistical strength.  If you need a RNG which an
+ * attacker can't predict, or which passes strong statistical tests, use the
+ * evutil_secure_rng* functions instead.
+ */
+ev_uint32_t evutil_weakrand_seed_(struct evutil_weakrand_state *state, ev_uint32_t seed);
+/* Return a pseudorandom value between 0 and EVUTIL_WEAKRAND_MAX inclusive.
+ * Updates the state in 'seed' as needed -- this value must be protected by a
+ * lock.
+ */
+ev_int32_t evutil_weakrand_(struct evutil_weakrand_state *seed);
+/* Return a pseudorandom value x such that 0 <= x < top. top must be no more
+ * than EVUTIL_WEAKRAND_MAX. Updates the state in 'seed' as needed -- this
+ * value must be proteced by a lock */
+ev_int32_t evutil_weakrand_range_(struct evutil_weakrand_state *seed, ev_int32_t top);
 
 /* Evaluates to the same boolean value as 'p', and hints to the compiler that
  * we expect this value to be false. */
diff --git a/win32select.c b/win32select.c
index 441222f1..7be2389f 100644
--- a/win32select.c
+++ b/win32select.c
@@ -202,6 +202,8 @@ win32_init(struct event_base *base)
 	if (evsig_init_(base) < 0)
 		winop->signals_are_broken = 1;
 
+	evutil_weakrand_seed_(&base->weakrand_seed, 0);
+
 	return (winop);
  err:
 	XFREE(winop->readset_in);
@@ -326,7 +328,8 @@ win32_dispatch(struct event_base *base, struct timeval *tv)
 	}
 
 	if (win32op->readset_out->fd_count) {
-		i = rand() % win32op->readset_out->fd_count;
+		i = evutil_weakrand_range_(&base->weakrand_seed,
+		    win32op->readset_out->fd_count);
 		for (j=0; j<win32op->readset_out->fd_count; ++j) {
 			if (++i >= win32op->readset_out->fd_count)
 				i = 0;
@@ -335,7 +338,8 @@ win32_dispatch(struct event_base *base, struct timeval *tv)
 		}
 	}
 	if (win32op->exset_out->fd_count) {
-		i = rand() % win32op->exset_out->fd_count;
+		i = evutil_weakrand_range_(&base->weakrand_seed,
+		    win32op->exset_out->fd_count);
 		for (j=0; j<win32op->exset_out->fd_count; ++j) {
 			if (++i >= win32op->exset_out->fd_count)
 				i = 0;
@@ -345,7 +349,8 @@ win32_dispatch(struct event_base *base, struct timeval *tv)
 	}
 	if (win32op->writeset_out->fd_count) {
 		SOCKET s;
-		i = rand() % win32op->writeset_out->fd_count;
+		i = evutil_weakrand_range_(&base->weakrand_seed,
+		    win32op->writeset_out->fd_count);
 		for (j=0; j<win32op->writeset_out->fd_count; ++j) {
 			if (++i >= win32op->writeset_out->fd_count)
 				i = 0;