diff --git a/test/functional/wallet_fundrawtransaction.py b/test/functional/wallet_fundrawtransaction.py
index 4530ac92d051..8f0577ba739c 100755
--- a/test/functional/wallet_fundrawtransaction.py
+++ b/test/functional/wallet_fundrawtransaction.py
@@ -1023,19 +1023,19 @@ def test_external_inputs(self):
         high_input_weight = input_weight * 2
 
         # Funding should also work if the input weight is provided
-        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": input_weight}])
+        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": input_weight}], fee_rate=2)
         signed_tx = wallet.signrawtransactionwithwallet(funded_tx["hex"])
         signed_tx = self.nodes[0].signrawtransactionwithwallet(signed_tx["hex"])
         assert_equal(self.nodes[0].testmempoolaccept([signed_tx["hex"]])[0]["allowed"], True)
         assert_equal(signed_tx["complete"], True)
         # Reducing the weight should have a lower fee
-        funded_tx2 = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": low_input_weight}])
+        funded_tx2 = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": low_input_weight}], fee_rate=2)
         assert_greater_than(funded_tx["fee"], funded_tx2["fee"])
         # Increasing the weight should have a higher fee
-        funded_tx2 = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": high_input_weight}])
+        funded_tx2 = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": high_input_weight}], fee_rate=2)
         assert_greater_than(funded_tx2["fee"], funded_tx["fee"])
         # The provided weight should override the calculated weight when solving data is provided
-        funded_tx3 = wallet.fundrawtransaction(raw_tx, solving_data={"descriptors": [desc]}, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": high_input_weight}])
+        funded_tx3 = wallet.fundrawtransaction(raw_tx, solving_data={"descriptors": [desc]}, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": high_input_weight}], fee_rate=2)
         assert_equal(funded_tx2["fee"], funded_tx3["fee"])
         # The feerate should be met
         funded_tx4 = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": high_input_weight}], fee_rate=10)
@@ -1044,8 +1044,8 @@ def test_external_inputs(self):
         assert_fee_amount(funded_tx4["fee"], tx4_size, Decimal(0.0001))
 
         # Funding with weight at csuint boundaries should not cause problems
-        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": 255}])
-        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": 65539}])
+        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": 255}], fee_rate=2)
+        funded_tx = wallet.fundrawtransaction(raw_tx, input_sizes=[{"txid": ext_utxo["txid"], "vout": ext_utxo["vout"], "size": 65539}], fee_rate=2)
 
         self.nodes[2].unloadwallet("extfund")
 
@@ -1294,7 +1294,9 @@ def do_fund_send(target):
             assert signed_tx["complete"]
             decoded_tx = tester.decoderawtransaction(signed_tx["hex"])
             assert_equal(len(decoded_tx["vin"]), 3)
-            assert tester.testmempoolaccept([signed_tx["hex"]])[0]["allowed"]
+            # The fee pays -minrelaytxfee, which equals the default maxfeerate, on the size the wallet estimates.
+            # An ECDSA signature can be a byte shorter than estimated, which would exceed maxfeerate.
+            assert tester.testmempoolaccept([signed_tx["hex"]], maxfeerate=0)[0]["allowed"]
 
         # We want to choose more value than is available in 2 inputs when considering the fee,
         # but not enough to need 3 inputs when not considering the fee.