diff --git a/bitcoin/signature.c b/bitcoin/signature.c
index 362e53551..2b6c7c29f 100644
--- a/bitcoin/signature.c
+++ b/bitcoin/signature.c
@@ -88,30 +88,19 @@ void sign_hash(const struct privkey *privkey,
 }
 
 /* Only does SIGHASH_ALL */
-static void sha256_tx_one_input(struct bitcoin_tx *tx,
+static void sha256_tx_one_input(const struct bitcoin_tx *tx,
 				size_t input_num,
 				const u8 *script,
 				const u8 *witness_script,
 				struct sha256_double *hash)
 {
-	size_t i;
-
 	assert(input_num < tal_count(tx->input));
 
-	/* You must have all inputs zeroed to start. */
-	for (i = 0; i < tal_count(tx->input); i++)
-		assert(!tx->input[i].script);
-
-	tx->input[input_num].script = cast_const(u8 *, script);
-
-	sha256_tx_for_sig(hash, tx, input_num, witness_script);
-
-	/* Reset it for next time. */
-	tx->input[input_num].script = NULL;
+	sha256_tx_for_sig(hash, tx, input_num, script, witness_script);
 }
 
 /* Only does SIGHASH_ALL */
-void sign_tx_input(struct bitcoin_tx *tx,
+void sign_tx_input(const struct bitcoin_tx *tx,
 		   unsigned int in,
 		   const u8 *subscript,
 		   const u8 *witness_script,
@@ -137,7 +126,7 @@ bool check_signed_hash(const struct sha256_double *hash,
 	return ret == 1;
 }
 
-bool check_tx_sig(struct bitcoin_tx *tx, size_t input_num,
+bool check_tx_sig(const struct bitcoin_tx *tx, size_t input_num,
 		  const u8 *redeemscript,
 		  const u8 *witness_script,
 		  const struct pubkey *key,
diff --git a/bitcoin/signature.h b/bitcoin/signature.h
index c3608cc4e..cfa58ef49 100644
--- a/bitcoin/signature.h
+++ b/bitcoin/signature.h
@@ -26,8 +26,7 @@ bool check_signed_hash(const struct sha256_double *hash,
 		       const secp256k1_ecdsa_signature *signature,
 		       const struct pubkey *key);
 
-/* All tx input scripts must be set to 0 len. */
-void sign_tx_input(struct bitcoin_tx *tx,
+void sign_tx_input(const struct bitcoin_tx *tx,
 		   unsigned int in,
 		   const u8 *subscript,
 		   const u8 *witness,
@@ -35,7 +34,7 @@ void sign_tx_input(struct bitcoin_tx *tx,
 		   secp256k1_ecdsa_signature *sig);
 
 /* Does this sig sign the tx with this input for this pubkey. */
-bool check_tx_sig(struct bitcoin_tx *tx, size_t input_num,
+bool check_tx_sig(const struct bitcoin_tx *tx, size_t input_num,
 		  const u8 *redeemscript,
 		  const u8 *witness,
 		  const struct pubkey *key,
diff --git a/bitcoin/tx.c b/bitcoin/tx.c
index b0495b737..28bb82bfa 100644
--- a/bitcoin/tx.c
+++ b/bitcoin/tx.c
@@ -14,11 +14,12 @@
 #define SEGREGATED_WITNESS_FLAG 0x1
 
 static void push_tx_input(const struct bitcoin_tx_input *input,
-			 void (*push)(const void *, size_t, void *), void *pushp)
+			  const u8 *input_script,
+			  void (*push)(const void *, size_t, void *), void *pushp)
 {
 	push(&input->txid, sizeof(input->txid), pushp);
 	push_le32(input->index, push, pushp);
-	push_varint_blob(input->script, push, pushp);
+	push_varint_blob(input_script, push, pushp);
 	push_le32(input->sequence_number, push, pushp);
 }
 
@@ -78,9 +79,15 @@ static void push_witnesses(const struct bitcoin_tx *tx,
 	}
 }
 
+/* For signing, we ignore input scripts on other inputs, and pretend
+ * the current input has a certain script: this is indicated by a
+ * non-NULL override_script, and setting override_script_index to the
+ * input number to replace. */
 static void push_tx(const struct bitcoin_tx *tx,
-		   void (*push)(const void *, size_t, void *), void *pushp,
-		   bool bip144)
+		    const u8 *override_script,
+		    size_t override_script_index,
+		    void (*push)(const void *, size_t, void *), void *pushp,
+		    bool bip144)
 {
 	varint_t i;
 	u8 flag = 0;
@@ -102,8 +109,16 @@ static void push_tx(const struct bitcoin_tx *tx,
 	}
 
 	push_varint(tal_count(tx->input), push, pushp);
-	for (i = 0; i < tal_count(tx->input); i++)
-		push_tx_input(&tx->input[i], push, pushp);
+	for (i = 0; i < tal_count(tx->input); i++) {
+		const u8 *input_script = tx->input[i].script;
+		if (override_script) {
+			if (override_script_index == i)
+				input_script = override_script;
+			else
+				input_script = NULL;
+		}
+		push_tx_input(&tx->input[i], input_script, push, pushp);
+	}
 
 	push_varint(tal_count(tx->output), push, pushp);
 	for (i = 0; i < tal_count(tx->output); i++)
@@ -216,23 +231,19 @@ static void hash_for_segwit(struct sha256_ctx *ctx,
 
 void sha256_tx_for_sig(struct sha256_double *h, const struct bitcoin_tx *tx,
 		       unsigned int input_num,
+		       const u8 *script,
 		       const u8 *witness_script)
 {
-	size_t i;
 	struct sha256_ctx ctx = SHA256_INIT;
 
-	/* Caller should zero-out other scripts for signing! */
 	assert(input_num < tal_count(tx->input));
-	for (i = 0; i < tal_count(tx->input); i++)
-		if (i != input_num)
-			assert(!tx->input[i].script);
 
 	if (witness_script) {
 		/* BIP143 hashing if OP_CHECKSIG is inside witness. */
 		hash_for_segwit(&ctx, tx, input_num, witness_script);
 	} else {
 		/* Otherwise signature hashing never includes witness. */
-		push_tx(tx, push_sha, &ctx, false);
+		push_tx(tx, script, input_num, push_sha, &ctx, false);
 	}
 
 	sha256_le32(&ctx, SIGHASH_ALL);
@@ -251,7 +262,7 @@ static void push_linearize(const void *data, size_t len, void *pptr_)
 u8 *linearize_tx(const tal_t *ctx, const struct bitcoin_tx *tx)
 {
 	u8 *arr = tal_arr(ctx, u8, 0);
-	push_tx(tx, push_linearize, &arr, true);
+	push_tx(tx, NULL, 0, push_linearize, &arr, true);
 	return arr;
 }
 
@@ -263,7 +274,7 @@ static void push_measure(const void *data UNUSED, size_t len, void *lenp)
 size_t measure_tx_weight(const struct bitcoin_tx *tx)
 {
 	size_t non_witness_len = 0, witness_len = 0;
-	push_tx(tx, push_measure, &non_witness_len, false);
+	push_tx(tx, NULL, 0, push_measure, &non_witness_len, false);
 	if (uses_witness(tx)) {
 		push_witnesses(tx, push_measure, &witness_len);
 		/* Include BIP 144 marker and flag bytes in witness length */
@@ -279,7 +290,7 @@ void bitcoin_txid(const struct bitcoin_tx *tx, struct bitcoin_txid *txid)
 	struct sha256_ctx ctx = SHA256_INIT;
 
 	/* For TXID, we never use extended form. */
-	push_tx(tx, push_sha, &ctx, false);
+	push_tx(tx, NULL, 0, push_sha, &ctx, false);
 	sha256_double_done(&ctx, &txid->shad);
 }
 
diff --git a/bitcoin/tx.h b/bitcoin/tx.h
index 8c1813a27..28dd820bc 100644
--- a/bitcoin/tx.h
+++ b/bitcoin/tx.h
@@ -45,7 +45,9 @@ void bitcoin_txid(const struct bitcoin_tx *tx, struct bitcoin_txid *txid);
 
 /* Useful for signature code. */
 void sha256_tx_for_sig(struct sha256_double *h, const struct bitcoin_tx *tx,
-		       unsigned int input_num, const u8 *witness_script);
+		       unsigned int input_num,
+		       const u8 *script,
+		       const u8 *witness_script);
 
 /* Linear bytes of tx. */
 u8 *linearize_tx(const tal_t *ctx, const struct bitcoin_tx *tx);