But I am not convinced that it will use funds the new incoming transaction, I think that it will use same input(s) and make one of the original outputs a bit smaller.
Electrum allows you to add new inputs for bumping the transaction fee.
You can do so, even if the new inputs come from a transaction made later than the original transaction.
Also, you can click on "Show advanced setting" when bumping the fee and select the strategy.
![](https://ip.bitcointalk.org/?u=https%3A%2F%2Fi.imgur.com%2F2JEbmKm.jpg&t=665&c=wsDAf9ECAAp7PQ)
If you use the first option, there would be three cases:
1. If there's a change (which is sufficient) in the original transaction, electrum decrease the change.
2. If there is no change (or there's a change, but it's not sufficient) and there's another available UTXO in the wallet, electrum combines that UTXO with original input(s).
3. If there is no change (or there's a change, but it's not sufficient) and there is no other UTXO in the wallet, there is no option other than decreasing the payment amount.