diff --git a/close_tx.c b/close_tx.c
index 1f43d43e5..c5b9b8883 100644
--- a/close_tx.c
+++ b/close_tx.c
@@ -10,9 +10,13 @@ struct bitcoin_tx *create_close_tx(const tal_t *ctx,
 				   const struct sha256_double *anchor_txid,
 				   unsigned int anchor_index,
 				   u64 anchor_satoshis,
-				   uint64_t to_us, uint64_t to_them)
+				   uint64_t to_us, uint64_t to_them,
+				   uint64_t dust_limit)
 {
 	struct bitcoin_tx *tx;
+	size_t num_outputs = 0;
+
+	assert(to_us + to_them <= anchor_satoshis);
 
 	/* Now create close tx: one input, two outputs. */
 	tx = bitcoin_tx(ctx, 1, 2);
@@ -22,19 +26,28 @@ struct bitcoin_tx *create_close_tx(const tal_t *ctx,
 	tx->input[0].index = anchor_index;
 	tx->input[0].amount = tal_dup(tx->input, u64, &anchor_satoshis);
 
-	/* One output is to us. */
-	tx->output[0].amount = to_us;
-	tx->output[0].script = tal_dup_arr(tx, u8,
+	if (to_us >= dust_limit) {
+		/* One output is to us. */
+		tx->output[num_outputs].amount = to_us;
+		tx->output[num_outputs].script = tal_dup_arr(tx, u8,
 					   our_script, tal_count(our_script), 0);
+		num_outputs++;
+	}
 
-	/* Other output is to them. */
-	tx->output[1].amount = to_them;
-	tx->output[1].script = tal_dup_arr(tx, u8,
+	if (to_them >= dust_limit) {
+		/* Other output is to them. */
+		tx->output[num_outputs].amount = to_them;
+		tx->output[num_outputs].script = tal_dup_arr(tx, u8,
 					   their_script, tal_count(their_script),
 					   0);
+		num_outputs++;
+	}
 
-	assert(tx->output[0].amount + tx->output[1].amount <= anchor_satoshis);
+	/* Can't have no outputs at all! */
+	if (num_outputs == 0)
+		return tal_free(tx);
+	tal_resize(&tx->output, num_outputs);
 
-	permute_outputs(tx->output, 2, NULL);
+	permute_outputs(tx->output, num_outputs, NULL);
 	return tx;
 }
diff --git a/close_tx.h b/close_tx.h
index 34ecc22f3..e1d9b775b 100644
--- a/close_tx.h
+++ b/close_tx.h
@@ -15,5 +15,6 @@ struct bitcoin_tx *create_close_tx(const tal_t *ctx,
 				   const struct sha256_double *anchor_txid,
 				   unsigned int anchor_index,
 				   u64 anchor_satoshis,
-				   uint64_t to_us, uint64_t to_them);
+				   uint64_t to_us, uint64_t to_them,
+				   uint64_t dust_limit);
 #endif
diff --git a/daemon/peer.c b/daemon/peer.c
index a434e8e17..73f0fdd6b 100644
--- a/daemon/peer.c
+++ b/daemon/peer.c
@@ -4365,7 +4365,7 @@ struct bitcoin_tx *peer_create_close_tx(const tal_t *ctx,
 			       peer->anchor.index,
 			       peer->anchor.satoshis,
 			       cstate.side[LOCAL].pay_msat / 1000,
-			       cstate.side[REMOTE].pay_msat / 1000);
+			       cstate.side[REMOTE].pay_msat / 1000, 0);
 }
 
 /* Sets up the initial cstate and commit tx for both nodes: false if