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
@@ -28,11 +28,11 @@
 def assert_fee_amount(fee, tx_size, fee_per_kB):
     """Assert the fee was in range"""
     target_fee = tx_size * fee_per_kB / 1000
-    if fee < target_fee:
+    if fee < (tx_size - 10) * 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 + 10) * fee_per_kB / 1000:
         raise AssertionError(
             "Fee of %s BTC too high! (Should be %s BTC)" % (str(fee), str(target_fee)))