diff --git a/onchaind/onchain.c b/onchaind/onchain.c
index b763fe0fa..86ec76aa6 100644
--- a/onchaind/onchain.c
+++ b/onchaind/onchain.c
@@ -1,3 +1,4 @@
+#include <bitcoin/feerate.h>
 #include <bitcoin/script.h>
 #include <ccan/crypto/shachain/shachain.h>
 #include <ccan/mem/mem.h>
@@ -274,13 +275,31 @@ static struct bitcoin_tx *tx_to_us(const tal_t *ctx,
 			 + 1 + 3 + 73 + 0 + tal_len(wscript))
 		/ 1000;
 
-	/* Result is trivial?  Spent to OP_RETURN to avoid leaving dust. */
+	/* Result is trivial?  Spend with small feerate, but don't wait
+	 * around for it as it might not confirm. */
 	if (tx->output[0].amount < dust_limit_satoshis + fee) {
-		tx->output[0].amount = 0;
-		tx->output[0].script = scriptpubkey_opreturn(tx->output);
-		*tx_type = DONATING_TO_MINERS;
-	} else
-		tx->output[0].amount -= fee;
+		/* FIXME: We should use SIGHASH_NONE so others can take it */
+		fee = feerate_floor() * (measure_tx_weight(tx)
+				       + 1 + 3 + 73 + 0 + tal_len(wscript))
+			/ 1000;
+		/* This shouldn't happen (we don't set feerate below floor!),
+		 * but just in case. */
+		if (tx->output[0].amount < dust_limit_satoshis + fee) {
+			fee = tx->output[0].amount - dust_limit_satoshis;
+			status_broken("TX %s can't afford minimal feerate"
+				      "; setting fee to %"PRIu64,
+				      tx_type_name(*tx_type),
+				      fee);
+		} else
+			status_unusual("TX %s amount %"PRIu64" too small to"
+				       " pay reasonable fee, using minimal fee"
+				       " and ignoring",
+				       tx_type_name(*tx_type),
+				       out->satoshi);
+
+		*tx_type = IGNORING_TINY_PAYMENT;
+	}
+	tx->output[0].amount -= fee;
 
 	sign_tx_input(tx, 0, NULL, wscript, privkey, pubkey, &sig);
 	tx->input[0].witness = bitcoin_witness_sig_and_element(tx->input,
@@ -361,6 +380,13 @@ static void proposal_meets_depth(struct tracked_output *out)
 	wire_sync_write(REQ_FD,
 			take(towire_onchain_broadcast_tx(NULL,
 							 out->proposal->tx)));
+
+	/* Don't wait for this if we're ignoring the tiny payment. */
+	if (out->proposal->tx_type == IGNORING_TINY_PAYMENT) {
+		ignore_output(out);
+		out->proposal = tal_free(out->proposal);
+	}
+
 	/* We will get a callback when it's in a block. */
 }
 
diff --git a/onchaind/onchain_types.h b/onchaind/onchain_types.h
index 78cd342fa..58f8ba750 100644
--- a/onchaind/onchain_types.h
+++ b/onchaind/onchain_types.h
@@ -36,7 +36,7 @@ enum tx_type {
 	OUR_PENALTY_TX,
 
 	/* Amount too small, we're just spending it to close UTXO */
-	DONATING_TO_MINERS,
+	IGNORING_TINY_PAYMENT,
 
 	/* Special type for marking outputs as resolved by self. */
 	SELF,
diff --git a/onchaind/test/run-grind_feerate.c b/onchaind/test/run-grind_feerate.c
index d67e5961a..0fbb8006f 100644
--- a/onchaind/test/run-grind_feerate.c
+++ b/onchaind/test/run-grind_feerate.c
@@ -108,6 +108,10 @@ bool per_commit_point(const struct sha256 *shaseed UNNEEDED,
 void status_failed(enum status_failreason code UNNEEDED,
 		   const char *fmt UNNEEDED, ...)
 { fprintf(stderr, "status_failed called!\n"); abort(); }
+/* Generated stub for status_fmt */
+void status_fmt(enum log_level level UNNEEDED, const char *fmt UNNEEDED, ...)
+
+{ fprintf(stderr, "status_fmt called!\n"); abort(); }
 /* Generated stub for status_setup_sync */
 void status_setup_sync(int fd UNNEEDED)
 { fprintf(stderr, "status_setup_sync called!\n"); abort(); }
diff --git a/tests/test_lightningd.py b/tests/test_lightningd.py
index 118db2de2..ce1d43273 100644
--- a/tests/test_lightningd.py
+++ b/tests/test_lightningd.py
@@ -2206,26 +2206,22 @@ class LightningDTests(BaseLightningDTests):
         l2.daemon.wait_for_log(' to ONCHAIN')
 
         # Wait for timeout.
-        l1.daemon.wait_for_log('Propose handling THEIR_UNILATERAL/OUR_HTLC by DONATING_TO_MINERS .* after 6 blocks')
-        bitcoind.generate_block(6)
-
-        l1.daemon.wait_for_log('sendrawtx exit 0')
-        bitcoind.generate_block(1)
+        l1.daemon.wait_for_log('Propose handling THEIR_UNILATERAL/OUR_HTLC by IGNORING_TINY_PAYMENT .* after 6 blocks')
+        bitcoind.generate_block(5)
 
-        l1.daemon.wait_for_log('Resolved THEIR_UNILATERAL/OUR_HTLC by our proposal DONATING_TO_MINERS')
+        l1.daemon.wait_for_logs(['Broadcasting IGNORING_TINY_PAYMENT .* to resolve THEIR_UNILATERAL/OUR_HTLC',
+                                 'sendrawtx exit 0',
+                                 'Ignoring output 0 of .*: THEIR_UNILATERAL/OUR_HTLC'])
 
         # 100 deep and l2 forgets.
-        bitcoind.generate_block(91)
-        sync_blockheight([l2])
+        bitcoind.generate_block(93)
+        sync_blockheight([l1, l2])
         assert not l2.daemon.is_in_log('onchaind complete, forgetting peer')
+        assert not l1.daemon.is_in_log('onchaind complete, forgetting peer')
         bitcoind.generate_block(1)
         l2.daemon.wait_for_log('onchaind complete, forgetting peer')
 
-        # l1 forgets 100 blocks after DONATING_TO_MINERS.
-        bitcoind.generate_block(6)
-        sync_blockheight([l1])
-        assert not l1.daemon.is_in_log('onchaind complete, forgetting peer')
-        bitcoind.generate_block(1)
+        # l1 does not wait for ignored payment.
         l1.daemon.wait_for_log('onchaind complete, forgetting peer')
 
     @unittest.skipIf(not DEVELOPER, "needs DEVELOPER=1 for dev_fail")