If you are going to make an offer and realize that you are already getting a good deal, go ahead an make your best offer because you might only get one shot.
I just did a short sale, where the bpo was at $310k and sold the house for $275k Not the deal of the year
but a fair deal for both sides. The bank never countered they immediately accepted.
Try to find out from the other Agent what the BPO (Broker Price Opinion) came in at.
Depending on who the bank is they are typically accepting 80% to 90% of that bpo.
Also, Remember you are looking at buying a preforeclosure because you want a deal I suppose.
Don't let your emotions get involved. Set your offer price, if it doesn't work move on to the next home.
There is no standard for what you should offer. Being a short sale you know that the price is less than is owed but isn't neccessarily what the market value of the house is. It still could be high. If you want to give a lowball offer, have your realtor run comps for the property to support your offer. Also, if possible, have your realtor take pictures of the property from less flatering angles to help support the offer. If you don't have a realtor I strongly suggest you get one and ideally one that has experience with short sales. Our office has had several short sales recently where the banks appraisal was higher than the asking price and we were able to get them to accept our offer for below asking price by doing what I just described. Also make sure that you are already pre-approved for a loan that will cover your offer (or letter from your bank stating you have enough funds for a cash deal). The more you can show you are a ready, willing and able buyer making an honest offer, and not just someone fishing for a deal, the better your chances. It still may take awhile for the bank to respond, but all this helps to speed up the process.
Offer what you think is fair for you and see what happens! :)