Short Sales are more successful when your offer is within 10% of BPO. If the broker asked to do the BPO takes in account the rehab, then you should have no problem getting a decent price.
To get below the a "lowball" offer accepted you should concentrate on writing a proposal when submitting your offer to the listing agent. In that proposal, include your justifications for your price. Be prepared to provide documentation. Investors who get their offers accepted are very good at justifying their price. Here you need to be creative.
Also, during the short sale process, most agents will submit all offers, but there may be some qualifying factors the lender may require. For instance, proof of funds may be stipulated.
Since there are a lot of variables, such as, lenders, markets, staffing, personality, etc., each deal is different from the last. One thing is constant though, convincing the lender it is in their best interest to sell the property to you at your price. The motivation for lenders to short sell are varied too. Some argue that carrying non-performing loans on the books hinder the banks ability to lend by tying up liquidity. Unfortunately, banks are illiquid on such a large scale in today's enviroment, that the case by case basis that is short sales, will not even be a drop in the proverbial bucket. So, I personally do not think this is a motivation for them anymore. I believe, in today's enviroment, the lender has to be convinced that the stand to lose more if they decide to wait until foreclosure.
Bank owned properties are a different animal. The lender has already added considerable expense in the judicial foreclosure process. Therefore, they may be less wlling to discount their properties.
Most agents will submit any reasonable offer, but it is difficult to get really big discounts here. Again, within 10% is very possible, but it really depends on DOM and other factors as well.
Good luck