diff --git a/electrum/gui/qml/qetxfinalizer.py b/electrum/gui/qml/qetxfinalizer.py
index 5e691732a..76a17ddec 100644
--- a/electrum/gui/qml/qetxfinalizer.py
+++ b/electrum/gui/qml/qetxfinalizer.py
@@ -888,10 +888,12 @@ class QETxCpfpFeeBumper(TxFeeSlider, TxMonMixin):
         if fee_per_kb is None:
             return None
         package_fee = FeePolicy.estimate_fee_for_feerate(fee_per_kb=fee_per_kb, size=self._total_size)
-        fee = package_fee - self._parent_fee
-        fee = min(self._max_fee, fee)
-        fee = max(self._total_size, fee)  # pay at least 1 sat/byte for combined size
-        return fee
+        child_fee = package_fee - self._parent_fee
+        child_fee = min(self._max_fee, child_fee)
+        # pay at least minrelayfee for combined size:
+        min_child_fee = FeePolicy.estimate_fee_for_feerate(fee_per_kb=self._wallet.wallet.relayfee(), size=self._total_size)
+        child_fee = max(min_child_fee, child_fee)
+        return child_fee
 
     def tx_verified(self):
         self._valid = False
diff --git a/electrum/gui/qt/main_window.py b/electrum/gui/qt/main_window.py
index 21c5c286e..a2aaf6a98 100644
--- a/electrum/gui/qt/main_window.py
+++ b/electrum/gui/qt/main_window.py
@@ -2875,10 +2875,12 @@ class ElectrumWindow(QMainWindow, MessageBoxMixin, Logger, QtEventListener):
             if fee_per_kb is None:
                 return None
             package_fee = FeePolicy.estimate_fee_for_feerate(fee_per_kb=fee_per_kb, size=total_size)
-            fee = package_fee - parent_fee
-            fee = min(max_fee, fee)
-            fee = max(total_size, fee)  # pay at least 1 sat/byte for combined size
-            return fee
+            child_fee = package_fee - parent_fee
+            child_fee = min(max_fee, child_fee)
+            # pay at least minrelayfee for combined size:
+            min_child_fee = FeePolicy.estimate_fee_for_feerate(fee_per_kb=self.wallet.relayfee(), size=total_size)
+            child_fee = max(min_child_fee, child_fee)
+            return child_fee
         fee_policy = FeePolicy(self.config.FEE_POLICY)
         suggested_feerate = fee_policy.fee_per_kb(self.network)
         fee = get_child_fee_from_total_feerate(suggested_feerate)