The 1856-O boasts a fairly substantial mintage of 1.1 million pieces but, because the New Orleans Mint was so far from collectors, the number of Mint State examples is less than expected. In fact, the 1856-O Half Dime is valued about the same as the 1855-O With Arrows, which has a lower mintage and is more in-demand as a type coin. Gem examples of this date are extremely rare and the best examples reported are a pair of PCGS MS66s.
Don't expect much out of the strike on 1856-O Half Dimes. The denticles are almost always weak, and the stars and wreath often lack detail, as well.