diff --git a/changes/bug2716 b/changes/bug2716
new file mode 100644
index 0000000000..4663ed3184
--- /dev/null
+++ b/changes/bug2716
@@ -0,0 +1,5 @@
+  o Minor features:
+    - When a relay has failed several reachability tests, be more accurate
+      at recording when it became unreachable, so we can in turn provide
+      more accuracy at assigning Stable, Guard, HSDir, etc flags. Bugfix
+      on 0.2.0.6-alpha. Resolves bug 2716.
diff --git a/src/or/dirserv.c b/src/or/dirserv.c
index aeeab45383..73869273a3 100644
--- a/src/or/dirserv.c
+++ b/src/or/dirserv.c
@@ -970,7 +970,11 @@ dirserv_set_router_is_running(routerinfo_t *router, time_t now)
 
   if (!answer && running_long_enough_to_decide_unreachable()) {
     /* not considered reachable. tell rephist. */
-    rep_hist_note_router_unreachable(router->cache_info.identity_digest, now);
+    time_t when = now;
+    if (router->last_reachable &&
+        router->last_reachable + REACHABILITY_TEST_PERIOD < now)
+      when = router->last_reachable + REACHABILITY_TEST_PERIOD;
+    rep_hist_note_router_unreachable(router->cache_info.identity_digest, when);
   }
 
   router->is_running = answer;
@@ -3187,7 +3191,8 @@ dirserv_single_reachability_test(time_t now, routerinfo_t *router)
  * try a few connections per call.
  *
  * The load balancing is such that if we get called once every ten
- * seconds, we will cycle through all the tests in 1280 seconds (a
+ * seconds, we will cycle through all the tests in
+ * 10*REACHABILITY_MASK_PER_TEST seconds (a
  * bit over 20 minutes).
  */
 void
@@ -3214,11 +3219,11 @@ dirserv_test_reachability(time_t now)
       continue; /* bridge authorities only test reachability on bridges */
 //    if (router->cache_info.published_on > cutoff)
 //      continue;
-    if ((((uint8_t)id_digest[0]) % 128) == ctr) {
+    if ((((uint8_t)id_digest[0]) % REACHABILITY_MODULO_PER_TEST) == ctr) {
       dirserv_single_reachability_test(now, router);
     }
   } SMARTLIST_FOREACH_END(router);
-  ctr = (ctr + 1) % 128; /* increment ctr */
+  ctr = (ctr + 1) % REACHABILITY_MODULO_PER_TEST; /* increment ctr */
 }
 
 /** Given a fingerprint <b>fp</b> which is either set if we're looking for a
diff --git a/src/or/dirserv.h b/src/or/dirserv.h
index 56ad7a6a56..949482ba73 100644
--- a/src/or/dirserv.h
+++ b/src/or/dirserv.h
@@ -12,6 +12,14 @@
 #ifndef _TOR_DIRSERV_H
 #define _TOR_DIRSERV_H
 
+/** What fraction (1 over this number) of the relay ID space do we
+ * (as a directory authority) launch connections to at each reachability
+ * test? */
+#define REACHABILITY_MODULO_PER_TEST 128
+
+/** How many seconds apart are the reachability tests for a given relay? */
+#define REACHABILITY_TEST_PERIOD (10*REACHABILITY_MODULO_PER_TEST)
+
 /** Maximum length of an exit policy summary. */
 #define MAX_EXITPOLICY_SUMMARY_LEN 1000
 
diff --git a/src/or/main.c b/src/or/main.c
index 979a2bec5c..558608ec8c 100644
--- a/src/or/main.c
+++ b/src/or/main.c
@@ -962,8 +962,9 @@ run_scheduled_events(time_t now)
   if (accounting_is_enabled(options))
     accounting_run_housekeeping(now);
 
-  if (now % 10 == 0 && (authdir_mode_tests_reachability(options)) &&
-      !we_are_hibernating()) {
+  if (now % REACHABILITY_TEST_PERIOD/REACHABILITY_MODULO_PER_TEST == 0 &&
+      (authdir_mode_tests_reachability(options)) &&
+       !we_are_hibernating()) {
     /* try to determine reachability of the other Tor relays */
     dirserv_test_reachability(now);
   }