Ivan,
Why not just allow the creditor to draft the funds directly from the account you wish to use? It is usually free, so long as you have sufficient funds in the account to cover the draft. You can usually instruct the mortgage company to draw the funds on any day from the first to the seventh with no additional fee; for dates after the seventh, there will be an added fee typically.
That should give you the same end result: bill payment without having to snail mail a check. But there is one added bonus! If the creditor does not draw the money on the specified date, and instead gets it late by say a day or a few, there is no late fee. If your online bill pay gives them the money late, you get to pay the late fee. In other words: the creditor is considered late in this arrangement, not the bill payer. Of course, you would still be required to have sufficient funds present in the account to cover, otherwise you do become considered late as the bill payer.