diff --git a/src/or/conscache.c b/src/or/conscache.c
index c30d1998c6..350a05b0f2 100644
--- a/src/or/conscache.c
+++ b/src/or/conscache.c
@@ -54,6 +54,11 @@ struct consensus_cache_t {
   storage_dir_t *dir;
   /** List of all the entries in the directory. */
   smartlist_t *entries;
+
+  /** The maximum number of entries that we'd like to allow in this cache.
+   * This is the same as the storagedir limit when MUST_UNMAP_TO_UNLINK is
+   * not defined. */
+  unsigned max_entries;
 };
 
 static void consensus_cache_clear(consensus_cache_t *cache);
@@ -71,6 +76,10 @@ consensus_cache_open(const char *subdir, int max_entries)
 {
   consensus_cache_t *cache = tor_malloc_zero(sizeof(consensus_cache_t));
   char *directory = get_datadir_fname(subdir);
+  cache->max_entries = max_entries;
+#ifdef MUST_UNMAP_TO_UNLINK
+  max_entries = 1000000;
+#endif
   cache->dir = storage_dir_new(directory, max_entries);
   tor_free(directory);
   if (!cache->dir) {
@@ -82,6 +91,19 @@ consensus_cache_open(const char *subdir, int max_entries)
   return cache;
 }
 
+/** Return true if it's okay to put more entries in this cache than
+ * its official file limit. */
+int
+consensus_cache_may_overallocate(consensus_cache_t *cache)
+{
+  (void) cache;
+#ifdef MUST_UNMAP_TO_UNLINK
+  return 1;
+#else
+  return 0;
+#endif
+}
+
 /**
  * Tell the sandbox (if any) configured by <b>cfg</b> to allow the
  * operations that <b>cache</b> will need.
@@ -90,6 +112,11 @@ int
 consensus_cache_register_with_sandbox(consensus_cache_t *cache,
                                       struct sandbox_cfg_elem **cfg)
 {
+#ifdef MUST_UNMAP_TO_UNLINK
+  /* Our sandbox doesn't support huge limits like we use here.
+   */
+  tor_assert_nonfatal_unreached();
+#endif
   return storage_dir_register_with_sandbox(cache->dir, cfg);
 }
 
diff --git a/src/or/conscache.h b/src/or/conscache.h
index aef54201f0..a0d74c4e08 100644
--- a/src/or/conscache.h
+++ b/src/or/conscache.h
@@ -14,6 +14,7 @@ HANDLE_DECL(consensus_cache_entry, consensus_cache_entry_t, )
 consensus_cache_t *consensus_cache_open(const char *subdir, int max_entries);
 void consensus_cache_free(consensus_cache_t *cache);
 struct sandbox_cfg_elem;
+int consensus_cache_may_overallocate(consensus_cache_t *cache);
 int consensus_cache_register_with_sandbox(consensus_cache_t *cache,
                                           struct sandbox_cfg_elem **cfg);
 void consensus_cache_unmap_lazy(consensus_cache_t *cache, time_t cutoff);
diff --git a/src/or/consdiffmgr.c b/src/or/consdiffmgr.c
index 928fc26f54..831d5d45c3 100644
--- a/src/or/consdiffmgr.c
+++ b/src/or/consdiffmgr.c
@@ -1136,7 +1136,7 @@ consdiffmgr_ensure_space_for_files(int n)
     return 0;
   }
   // Let's get more assertive: clean out unused stuff, and force-remove
-  // the files.
+  // the files that we can.
   consdiffmgr_cleanup();
   consensus_cache_delete_pending(cache, 1);
   const int n_to_remove = n - consensus_cache_get_n_filenames_available(cache);
@@ -1159,6 +1159,14 @@ consdiffmgr_ensure_space_for_files(int n)
   smartlist_free(objects);
 
   consensus_cache_delete_pending(cache, 1);
+
+  if (consensus_cache_may_overallocate(cache)) {
+    /* If we're allowed to throw extra files into the cache, let's do so
+     * rather getting upset.
+     */
+    return 0;
+  }
+
   if (BUG(n_marked < n_to_remove))
     return -1;
   else