diff --git a/state.c b/state.c
index 6a2c2e027..a88e55ca3 100644
--- a/state.c
+++ b/state.c
@@ -153,19 +153,24 @@ struct state_effect *state(const tal_t *ctx,
 		}
 		break;
 	case STATE_OPEN_WAITING_OURANCHOR:
+		if (input_is(input, PKT_OPEN_COMPLETE)) {
+			return next_state(ctx, effect,
+					  STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED);
+		}
+	/* Fall thru */
+	case STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED:
 		if (input_is(input, BITCOIN_ANCHOR_DEPTHOK)) {
 			add_effect(&effect, send_pkt,
 				   pkt_open_complete(ctx, peer));
+			if (state == STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED) {
+				add_effect(&effect, cmd_success, CMD_OPEN_WITH_ANCHOR);
+				return next_state(ctx, effect, STATE_NORMAL_HIGHPRIO);
+			}
 			return next_state(ctx, effect,
 					  STATE_OPEN_WAIT_FOR_COMPLETE_OURANCHOR);
 		} else if (input_is(input, BITCOIN_ANCHOR_UNSPENT)) {
 			add_effect(&effect, cmd_fail, NULL);
 			goto anchor_unspent;
-		} else if (input_is(input, PKT_OPEN_COMPLETE)) {
-			/* Ignore until we've hit depth ourselves. */
-			add_effect(&effect, cmd_defer, input);
-			/* No state change. */
-			return effect;
 		} else if (input_is(input, BITCOIN_ANCHOR_THEIRSPEND)) {
 			/* We no longer care about anchor depth. */
 			add_effect(&effect, unwatch,
@@ -204,6 +209,12 @@ struct state_effect *state(const tal_t *ctx,
 		}
 		break;
 	case STATE_OPEN_WAITING_THEIRANCHOR:
+		if (input_is(input, PKT_OPEN_COMPLETE)) {
+			return next_state(ctx, effect,
+					  STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED);
+		}
+	/* Fall thru */
+	case STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED:
 		if (input_is(input, BITCOIN_ANCHOR_TIMEOUT)) {
 			/* Anchor didn't reach blockchain in reasonable time. */
 			add_effect(&effect, send_pkt,
@@ -212,6 +223,12 @@ struct state_effect *state(const tal_t *ctx,
 		} else if (input_is(input, BITCOIN_ANCHOR_DEPTHOK)) {
 			add_effect(&effect, send_pkt,
 				   pkt_open_complete(ctx, peer));
+			if (state == STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED) {
+				add_effect(&effect, cmd_success,
+					   CMD_OPEN_WITHOUT_ANCHOR);
+				return next_state(ctx, effect,
+						  STATE_NORMAL_LOWPRIO);
+			}
 			return next_state(ctx, effect, STATE_OPEN_WAIT_FOR_COMPLETE_THEIRANCHOR);
 		} else if (input_is(input, BITCOIN_ANCHOR_UNSPENT)) {
 			add_effect(&effect, cmd_fail, NULL);
@@ -227,11 +244,6 @@ struct state_effect *state(const tal_t *ctx,
 						     BITCOIN_ANCHOR_TIMEOUT));
 			add_effect(&effect, cmd_fail, NULL);
 			goto them_unilateral;
-		} else if (input_is(input, PKT_OPEN_COMPLETE)) {
-			/* Ignore until we've hit depth ourselves. */
-			add_effect(&effect, cmd_defer, input);
-			/* No state change. */
-			return effect;
 		} else if (input_is(input, CMD_CLOSE)) {
 			/* We no longer care about anchor depth. */
 			add_effect(&effect, unwatch,
diff --git a/state_types.h b/state_types.h
index 7322eb4df..36f7d1af4 100644
--- a/state_types.h
+++ b/state_types.h
@@ -23,6 +23,8 @@ enum state {
 	STATE_OPEN_WAIT_FOR_COMMIT_SIG,
 	STATE_OPEN_WAITING_OURANCHOR,
 	STATE_OPEN_WAITING_THEIRANCHOR,
+	STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED,
+	STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED,
 	STATE_OPEN_WAIT_FOR_COMPLETE_OURANCHOR,
 	STATE_OPEN_WAIT_FOR_COMPLETE_THEIRANCHOR,
 
diff --git a/test/test_state_coverage.c b/test/test_state_coverage.c
index a1ff01404..0a3df02e0 100644
--- a/test/test_state_coverage.c
+++ b/test/test_state_coverage.c
@@ -1858,13 +1858,17 @@ static const char *simplify_state(enum state s)
 
 static bool waiting_statepair(enum state a, enum state b)
 {
-	if (a > b)
-		return waiting_statepair(b, a);
-
 	/* We don't need inputs if we're waiting for anchors. */
-	if (a == STATE_OPEN_WAITING_OURANCHOR)
+	if (a == STATE_OPEN_WAITING_OURANCHOR
+	    || a == STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED
+	    || a == STATE_OPEN_WAITING_THEIRANCHOR
+	    || a == STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED)
 		return true;
-	if (b == STATE_OPEN_WAITING_THEIRANCHOR)
+
+	if (b == STATE_OPEN_WAITING_OURANCHOR
+	    || b == STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED
+	    || b == STATE_OPEN_WAITING_THEIRANCHOR
+	    || b == STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED)
 		return true;
 
 	/* We don't need inputs at start of main loop. */
@@ -1872,6 +1876,10 @@ static bool waiting_statepair(enum state a, enum state b)
 	    && b == STATE_NORMAL_HIGHPRIO)
 		return true;
 
+	if (a == STATE_NORMAL_HIGHPRIO
+	    && b == STATE_NORMAL_LOWPRIO)
+		return true;
+
 	return false;
 }
 
@@ -2493,13 +2501,15 @@ int main(int argc, char *argv[])
 		if (i == STATE_OPEN_WAIT_FOR_OPEN_NOANCHOR
 		    || i == STATE_OPEN_WAIT_FOR_ANCHOR
 		    || i == STATE_OPEN_WAITING_THEIRANCHOR
+		    || i == STATE_OPEN_WAITING_THEIRANCHOR_THEYCOMPLETED
 		    || i == STATE_OPEN_WAIT_FOR_COMPLETE_THEIRANCHOR
 		    || i == STATE_ERR_ANCHOR_TIMEOUT)
 			a_expect = false;
 		if (i == STATE_OPEN_WAIT_FOR_OPEN_WITHANCHOR
 		    || i == STATE_OPEN_WAIT_FOR_COMMIT_SIG
 		    || i == STATE_OPEN_WAIT_FOR_COMPLETE_OURANCHOR
-		    || i == STATE_OPEN_WAITING_OURANCHOR)
+		    || i == STATE_OPEN_WAITING_OURANCHOR
+		    || i == STATE_OPEN_WAITING_OURANCHOR_THEYCOMPLETED)
 			b_expect = false;
 		if (i == STATE_ERR_INTERNAL)
 			a_expect = b_expect = false;