You've already shot for the moon with your first offer - and were denied. Your offer was so low that the lender didn't counter. Get a current, level-headed market analysis for the property and base your offer on that figure minus whatever you think the lender may term "an acceptable loss" - say 5-10% (maximum).
Remember that negotiating for a bank-owned property is much like attending a 1-person auction: You must guard against overbidding. If the property doesn't make sense at your calculated offering price or a counteroffer price, you have to be prepared to walk away and seek a better deal elsewhere.
Percentages wise I have seen banks all over the place. Some accept 15-20% under list price, others keep it 5-10% under list price. If there are multiple offers, I am still seeing homes that sell over the list price....even in the current buyers market
Thanks, Todd Norsted
Rosellen Dollahite-Auburn Ca.