Just because the owner of the Cardinals can afford to pay $25 million a year to Adam Wainwright, does that mean they should have offered that?  The same holds true in purchasing a home.  If you show a pre-approval letter that is for full asking price or more, does that mean the house is worth it full asking price or more?  Does that mean the seller thinks his house is worth his asking price?  Of course not!  It just means you are very well qualified to make offers.  What you can afford to pay is irrelevant to the value of a house.  

Do yourself a huge favor and have your lender prepare the letter for the maximum amount you can borrow, even if you don't want to spend that much.  It shows a seller that you can afford other higher-priced homes and gives the seller peace of mind that you are not even the least bit "tight on margins".  

Here is a very typical scenario when I am the Listing Agent and a Buyer's Agent presents an offer to us let's say for 8% under our asking price:  The Pre-Approval letter is---surprise!---exactly the same amount as the offer!!  So what does the Seller think of that?  1) You are playing a game and pretending this is all you can afford or 2) You really can't afford their house so don't waste our time negotiating if you aren't even approved for the asking price.  

What ends up happening is we counter the offer asking buyer to produce a letter that is for asking price or more and all we get is another letter for the bumped-up new counteroffer.  The seller has no idea if the buyer can really afford his house even though the Buyers Agent may be saying, "they are approved for more".  Then great, just give us the correct letter to start with and let's save the back and forth counteroffers requesting a correct pre-approval amount.