diff --git a/ssh.c b/ssh.c
index f5cf7142..2749f23f 100644
--- a/ssh.c
+++ b/ssh.c
@@ -8846,8 +8846,10 @@ static void do_ssh2_connection(void *vctx)
      * matches any of the table entries we've just modified will go to
      * the right handler function, and won't come here to confuse us.
      */
-    if (pq_empty_on_to_front_of(&ssh->pq_ssh2_connection, &ssh->pq_full))
+    if (pq_peek(&ssh->pq_ssh2_connection)) {
+        pq_concatenate(&ssh->pq_full, &ssh->pq_ssh2_connection, &ssh->pq_full);
         queue_idempotent_callback(&ssh->pq_full_consumer);
+    }
 
     /*
      * Now the connection protocol is properly up and running, with
diff --git a/ssh.h b/ssh.h
index 7ed45101..f4ef94ef 100644
--- a/ssh.h
+++ b/ssh.h
@@ -102,7 +102,8 @@ typedef struct PktOutQueue {
 void pq_base_init(PacketQueueBase *pqb);
 void pq_base_push(PacketQueueBase *pqb, PacketQueueNode *node);
 void pq_base_push_front(PacketQueueBase *pqb, PacketQueueNode *node);
-int pq_base_empty_on_to_front_of(PacketQueueBase *src, PacketQueueBase *dest);
+void pq_base_concatenate(PacketQueueBase *dest,
+                         PacketQueueBase *q1, PacketQueueBase *q2);
 
 void pq_in_init(PktInQueue *pq);
 void pq_out_init(PktOutQueue *pq);
@@ -117,10 +118,12 @@ void pq_out_clear(PktOutQueue *pq);
               pq_base_push_front(&(pq)->pqb, &(pkt)->qnode))
 #define pq_peek(pq) ((pq)->get(&(pq)->pqb, FALSE))
 #define pq_pop(pq) ((pq)->get(&(pq)->pqb, TRUE))
-#define pq_empty_on_to_front_of(src, dst)                               \
-    TYPECHECK((src)->get(&(src)->pqb, FALSE) ==                         \
+#define pq_concatenate(dst, q1, q2)                                      \
+    TYPECHECK((q1)->get(&(q1)->pqb, FALSE) ==                           \
+              (dst)->get(&(dst)->pqb, FALSE) &&                         \
+              (q2)->get(&(q2)->pqb, FALSE) ==                           \
               (dst)->get(&(dst)->pqb, FALSE),                           \
-              pq_base_empty_on_to_front_of(&(src)->pqb, &(dst)->pqb))
+              pq_base_concatenate(&(dst)->pqb, &(q1)->pqb, &(q2)->pqb))
 
 /*
  * Packet type contexts, so that ssh2_pkt_type can correctly decode
diff --git a/sshcommon.c b/sshcommon.c
index 7af086fe..856a8358 100644
--- a/sshcommon.c
+++ b/sshcommon.c
@@ -88,22 +88,66 @@ void pq_out_clear(PktOutQueue *pq)
         ssh_free_pktout(pkt);
 }
 
-int pq_base_empty_on_to_front_of(PacketQueueBase *src, PacketQueueBase *dest)
+/*
+ * Concatenate the contents of the two queues q1 and q2, and leave the
+ * result in qdest. qdest must be either empty, or one of the input
+ * queues.
+ */
+void pq_base_concatenate(PacketQueueBase *qdest,
+                         PacketQueueBase *q1, PacketQueueBase *q2)
 {
-    struct PacketQueueNode *srcfirst, *srclast;
+    struct PacketQueueNode *head1, *tail1, *head2, *tail2;
 
-    if (src->end.next == &src->end)
-        return FALSE;
+    /*
+     * Extract the contents from both input queues, and empty them.
+     */
 
-    srcfirst = src->end.next;
-    srclast = src->end.prev;
-    srcfirst->prev = &dest->end;
-    srclast->next = dest->end.next;
-    srcfirst->prev->next = srcfirst;
-    srclast->next->prev = srclast;
-    src->end.next = src->end.prev = &src->end;
+    head1 = (q1->end.next == &q1->end ? NULL : q1->end.next);
+    tail1 = (q1->end.prev == &q1->end ? NULL : q1->end.prev);
+    head2 = (q2->end.next == &q2->end ? NULL : q2->end.next);
+    tail2 = (q2->end.prev == &q2->end ? NULL : q2->end.prev);
 
-    return TRUE;
+    q1->end.next = q1->end.prev = &q1->end;
+    q2->end.next = q2->end.prev = &q2->end;
+
+    /*
+     * Link the two lists together, handling the case where one or
+     * both is empty.
+     */
+
+    if (tail1)
+        tail1->next = head2;
+    else
+        head1 = head2;
+
+    if (head2)
+        head2->prev = tail1;
+    else
+        tail2 = head1;
+
+    /*
+     * Check the destination queue is currently empty. (If it was one
+     * of the input queues, then it will be, because we emptied both
+     * of those just a moment ago.)
+     */
+
+    assert(qdest->end.next == &qdest->end);
+    assert(qdest->end.prev == &qdest->end);
+
+    /*
+     * If our concatenated list has anything in it, then put it in
+     * dest.
+     */
+
+    if (!head1) {
+        assert(!tail2);
+    } else {
+        assert(tail2);
+        qdest->end.next = head1;
+        qdest->end.prev = tail2;
+        head1->prev = &qdest->end;
+        tail2->next = &qdest->end;
+    }
 }
 
 /* ----------------------------------------------------------------------