Bob, don't lose heart! The fact that they waited for your offer is a good sign. Oftentimes when there are multiple offers the seller may once again come back with a "highest and best" request (even though they already said to submit it that way). You and your agent have to decide what the home is really worth, both in terms of market value and in terms of value to you personally (i.e. is it in a preferred neighborhood, near kids' schools, etc.) and decide on your final price in case this situation comes up. 15% over asking SEEMS like a very good offer, it just depends on who else is bidding against you and their offers. Be careful not to get too caught up in the highest and best situation, if they sense how much you want this home the seller could be bluffing to push the price higher. Be at peace with your offer as there are plenty of other homes on the market. Good luck!