diff --git a/changes/bug11553 b/changes/bug11553
new file mode 100644
index 0000000000..ed30ce9850
--- /dev/null
+++ b/changes/bug11553
@@ -0,0 +1,15 @@
+  o Minor features:
+    - When we run out of usable circuit IDs on a channel, log only one
+      warning for the whole channel, and include a description of
+      how many circuits there were on the channel. Fix for part of ticket
+      #11553.
+
+
+  o Major features (performance):
+    - Avoid wasting cycles looking for usable circuit IDs. Previously,
+      when allocating a new circuit ID, we would in the worst case do a
+      linear scan over the entire possible range of circuit IDs before
+      deciding that we had exhausted our possibilities. Now, we
+      try 64 circuit IDs at random before deciding that we probably
+      won't succeed. Fix for a possible root cause of ticket
+      #11553.
diff --git a/src/or/channel.c b/src/or/channel.c
index 32e87c342c..286154cb2c 100644
--- a/src/or/channel.c
+++ b/src/or/channel.c
@@ -728,9 +728,6 @@ channel_init(channel_t *chan)
   /* Init timestamp */
   chan->timestamp_last_added_nonpadding = time(NULL);
 
-  /* Init next_circ_id */
-  chan->next_circ_id = crypto_rand_int(1 << 15);
-
   /* Initialize queues. */
   TOR_SIMPLEQ_INIT(&chan->incoming_queue);
   TOR_SIMPLEQ_INIT(&chan->outgoing_queue);
diff --git a/src/or/channel.h b/src/or/channel.h
index 7ec222df0f..de19fad9a5 100644
--- a/src/or/channel.h
+++ b/src/or/channel.h
@@ -149,11 +149,8 @@ struct channel_s {
   circ_id_type_bitfield_t circ_id_type:2;
   /** DOCDOC*/
   unsigned wide_circ_ids:1;
-  /**
-   * Which circ_id do we try to use next on this connection?  This is
-   * always in the range 0..1<<15-1.
-   */
-  circid_t next_circ_id;
+  /** Have we logged a warning about circID exhaustion on this channel? */
+  unsigned warned_circ_ids_exhausted:1;
 
   /** For how many circuits are we n_chan?  What about p_chan? */
   unsigned int num_n_circuits, num_p_circuits;
diff --git a/src/or/circuitbuild.c b/src/or/circuitbuild.c
index 98fef4c142..e1d57ad6eb 100644
--- a/src/or/circuitbuild.c
+++ b/src/or/circuitbuild.c
@@ -77,18 +77,21 @@ channel_connect_for_circuit(const tor_addr_t *addr, uint16_t port,
   return chan;
 }
 
-/** Iterate over values of circ_id, starting from conn-\>next_circ_id,
- * and with the high bit specified by conn-\>circ_id_type, until we get
- * a circ_id that is not in use by any other circuit on that conn.
+
+/** Search for a value for circ_id that we can use on <b>chan</b> for an
+ * outbound circuit, until we get a circ_id that is not in use by any other
+ * circuit on that conn.
  *
  * Return it, or 0 if can't get a unique circ_id.
  */
 static circid_t
 get_unique_circ_id_by_chan(channel_t *chan)
 {
+#define MAX_CIRCID_ATTEMPTS 64
+
   circid_t test_circ_id;
   circid_t attempts=0;
-  circid_t high_bit, max_range;
+  circid_t high_bit, max_range, mask;
 
   tor_assert(chan);
 
@@ -98,23 +101,40 @@ get_unique_circ_id_by_chan(channel_t *chan)
              "a client with no identity.");
     return 0;
   }
-  max_range =  (chan->wide_circ_ids) ? (1u<<31) : (1u<<15);
+  max_range = (chan->wide_circ_ids) ? (1u<<31) : (1u<<15);
+  mask = max_range - 1;
   high_bit = (chan->circ_id_type == CIRC_ID_TYPE_HIGHER) ? max_range : 0;
   do {
-    /* Sequentially iterate over test_circ_id=1...max_range until we find a
-     * circID such that (high_bit|test_circ_id) is not already used. */
-    test_circ_id = chan->next_circ_id++;
-    if (test_circ_id == 0 || test_circ_id >= max_range) {
-      test_circ_id = 1;
-      chan->next_circ_id = 2;
-    }
-    if (++attempts > max_range) {
-      /* Make sure we don't loop forever if all circ_id's are used. This
-       * matters because it's an external DoS opportunity.
+    if (++attempts > MAX_CIRCID_ATTEMPTS) {
+      /* Make sure we don't loop forever because all circuit IDs are used.
+       *
+       * Once, we would try until we had tried every possible circuit ID.  But
+       * that's quite expensive.  Instead, we try MAX_CIRCID_ATTEMPTS random
+       * circuit IDs, and then give up.
+       *
+       * This potentially causes us to give up early if our circuit ID space
+       * is nearly full.  If we have N circuit IDs in use, then we will reject
+       * a new circuit with probability (N / max_range) ^ MAX_CIRCID_ATTEMPTS.
+       * This means that in practice, a few percent of our circuit ID capacity
+       * will go unused.
+       *
+       * The alternative here, though, is to do a linear search over the
+       * whole circuit ID space every time we extend a circuit, which is
+       * not so great either.
        */
-      log_warn(LD_CIRC,"No unused circ IDs. Failing.");
+      if (! chan->warned_circ_ids_exhausted) {
+        chan->warned_circ_ids_exhausted = 1;
+        log_warn(LD_CIRC,"No unused circIDs found on channel %s wide "
+                 "circID support, with %u inbound and %u outbound circuits. "
+                 "Failing a circuit.",
+                 chan->wide_circ_ids ? "with" : "without",
+                 chan->num_p_circuits, chan->num_n_circuits);
+      }
       return 0;
     }
+
+    crypto_rand((char*) &test_circ_id, sizeof(test_circ_id));
+    test_circ_id &= mask;
     test_circ_id |= high_bit;
   } while (circuit_id_in_use_on_channel(test_circ_id, chan));
   return test_circ_id;
diff --git a/src/or/connection.c b/src/or/connection.c
index 2e72e6b397..9614fa52da 100644
--- a/src/or/connection.c
+++ b/src/or/connection.c
@@ -271,8 +271,6 @@ dir_connection_new(int socket_family)
  *
  * Set timestamp_last_added_nonpadding to now.
  *
- * Assign a pseudorandom next_circ_id between 0 and 2**15.
- *
  * Initialize active_circuit_pqueue.
  *
  * Set active_circuit_pqueue_last_recalibrated to current cell_ewma tick.