First, if you have a Realtor, ask what is "normally acceptable" in that part of the country with regard to making an offer. Remember, if the house is advertised on a listing for 84, and the market value is much higher, you will probably need to show the bank "good reason" why you are going to offer less than the listing - especially if you are also wanting them to pay for closing costs as well. If the bank truly does have "several offers" the agent may be telling the truth or blowing smoke. If the listing agent is known to be of high moral and ethical character in the community, chances are that person is telling the truth. In my part of the country, an average home sells for roughly 5% less than the listing price. If the house is well priced considering its Fair Market Value (FMV), then give the bank close to what they are asking. You really need to get a BPO/APO or what is commonly called a "Broker Price Opinion/Agent Price Opinion" to really know what the best price to offer would (or should) be. Your Realtor should be able to assist you in this matter and then, based on having the information you need, PUT IN AN OFFER. Get that price opinion soon!