How about telling them that you did an extensive market analysis that indicated that it would sell for $X and the bank, because of your prior reputation for correct pricing, listed at your recommended price. Thus, if they offer full price the odds are good that they will get it unless someone else comes in over list.

I have used it before and it has worked. I also throw in that if they look at our solds in MLS they will see that 50+% of our listings go over list price with multiple offers because we are very aggressive with the banks on pricing.
Good Luck