Before revision:  In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design near-optimal mechanisms with provable, constant-factor approximation guarantees with just a{\em   single sample from the priors!
After revision:  In this work, we go one step further and show that for many fundamental two-sided markets-e.g., bilateral trade, double auctions, and combinatorial double auctions-it is possible to design near-optimal mechanisms with provable, constant-factor approximation guarantees with just a{\em (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from the priors!