diff --git a/changes/bug5508 b/changes/bug5508
new file mode 100644
index 0000000000..6606f822f2
--- /dev/null
+++ b/changes/bug5508
@@ -0,0 +1,4 @@
+  o Minor bugfixes:
+    - Fix a bug where a bridge authority crashes (on a failed assert)
+      if it has seen no directory requests when it's time to write
+      statistics to disk.
diff --git a/src/or/rephist.c b/src/or/rephist.c
index 3d5000ccf8..0cd60eeb83 100644
--- a/src/or/rephist.c
+++ b/src/or/rephist.c
@@ -2657,6 +2657,8 @@ rep_hist_format_desc_stats(time_t now)
     return NULL;
 
   size =  digestmap_size(served_descs);
+  if (size == 0)
+    return NULL;
   vals = tor_malloc(size * sizeof(int));
 
   for (iter = digestmap_iter_init(served_descs); !digestmap_iter_done(iter);