diff --git a/test/functional/fundrawtransaction.py b/test/functional/fundrawtransaction.py
--- a/test/functional/fundrawtransaction.py
+++ b/test/functional/fundrawtransaction.py
@@ -651,14 +651,18 @@
             rawtx)  # uses min_relay_tx_fee (set by settxfee)
         result2 = self.nodes[3].fundrawtransaction(
             rawtx, {"feeRate": 2 * min_relay_tx_fee})
-        result3 = self.nodes[3].fundrawtransaction(
-            rawtx, {"feeRate": 10 * min_relay_tx_fee})
         result_fee_rate = result['fee'] * 1000 / \
             FromHex(CTransaction(), result['hex']).billable_size()
         assert_fee_amount(
             result2['fee'], FromHex(CTransaction(), result2['hex']).billable_size(), 2 * result_fee_rate)
+
+        result3 = self.nodes[3].fundrawtransaction(
+            rawtx, {"feeRate": 10 * min_relay_tx_fee})
+        # allow this transaction to be underfunded by 10 bytes.  This is due
+        # to the first transaction possibly being overfunded by up to .9
+        # satoshi due to  fee ceilings being used.
         assert_fee_amount(
-            result3['fee'], FromHex(CTransaction(), result3['hex']).billable_size(), 10 * result_fee_rate)
+            result3['fee'], FromHex(CTransaction(), result3['hex']).billable_size(), 10 * result_fee_rate, 10)
 
         #
         # Test address reuse option #
diff --git a/test/functional/test_framework/util.py b/test/functional/test_framework/util.py
--- a/test/functional/test_framework/util.py
+++ b/test/functional/test_framework/util.py
@@ -25,14 +25,20 @@
 ##################
 
 
-def assert_fee_amount(fee, tx_size, fee_per_kB):
-    """Assert the fee was in range"""
+def assert_fee_amount(fee, tx_size, fee_per_kB, wiggleroom=2):
+    """
+    Assert the fee was in range
+
+    wiggleroom defines an amount that the test expects the wallet to be off by
+    when estimating fees.  This can be due to the dummy signature that is added
+    during fee calculation, or due to the wallet funding transactions using the
+    ceiling of the calculated fee.
+    """
     target_fee = tx_size * fee_per_kB / 1000
-    if fee < target_fee:
+    if fee < (tx_size - wiggleroom) * fee_per_kB / 1000:
         raise AssertionError(
             "Fee of %s BTC too low! (Should be %s BTC)" % (str(fee), str(target_fee)))
-    # allow the wallet's estimation to be at most 2 bytes off
-    if fee > (tx_size + 2) * fee_per_kB / 1000:
+    if fee > (tx_size + wiggleroom) * fee_per_kB / 1000:
         raise AssertionError(
             "Fee of %s BTC too high! (Should be %s BTC)" % (str(fee), str(target_fee)))