It's OK to put the maximum $ in your mortgage pre-approval letter.

Advice from Rugg Realty, Sun City Texas.

There seems to be a widely held belief that a buyer should have their mortgage preapproval letter only state the amount of their offer and no more. This requires a new/different preapproval letter for each offer made, and also necessitates (if the seller's agent is on top of things) a new preapproval letter if negotiations take the sales price higher. The logic is that a buyer should not give away the fact that they could afford more and therefore be forced in to a higher price because of the preapproval letter.  

This is hogwash.

Buyers want to make themselves appear as qualified as they possibly can. They should also be armed with a preapproval letter that can be used on any property and not be delayed waiting on a new version. The notion that a seller will expect more because the buyer can afford more is nonsense. My best demonstration of this is to use the Warren Buffet example:

If Warren Buffet came to your market and wanted to buy a residence, do you think he would over pay just because he may be able to afford more? Of course not. In fact, the seller might reasonably expect the negotiations to be weighted in favor of the buyer, who has lots of resources to perform due diligence and negotiate the very best terms in their favor.

Do yourself a favor and have a preapproval letter state what you are genuinly qualifed to borrow.  You'll be better off.