Unfortunately, every single one is a Short Sale!
The way the current market is, and Barry touched on this a little, is that anything under 500k is selling like hotcakes! Investors and first-time buyers (with all the government incentives) are coming out of the wood-work. Under 500k is truly a seller's market and because of that, conventional sale will probably not dip below 340k for what you are looking for.
Good luck on your search and let us know if you need anything!
The question you pose is an interesting one in today's (sellers) market. First, to be specific, YES it IS POSSIBLE to find a property as you describe for under $340K. There is one on the market currently, just listed on Friday (see link below). However, now that we have identified a potential property, which happens to be an REO listed at $322,400 are you willing to offer $340K for it?? I went to the house yesterday at 8am, and there was a stack of realtor cards on the kitchen counter. Since you are not the only qualified Buyer looking for a property in the mid-$300K range, and because inventory levels are obviously low, the concept of supply and demand weighs in heavily -- so expect this property to sell well above list price. The floors are terra-cotta tiles, there are vaulted ceilings & the lot is quite large, with a deep wash behind the property. The baths have been upgraded, too. Good luck in your quest for a home -- Expect the competition to follow you at least until the end of the year. Should interest rates continue to rise, this will cause some to drop out of the market until prices decline again.