This article has outlined a new approach for the simultaneous calculation of value-at-risk (VaR) and optimization of conditional VaR (CVaR) for a broad class of problems. We have shown that CVaR can be efficiently minimized using LP techniques. Our numerical experiments show that CVaR optimal portfolios are near optimal in VaR terms, i.e., VaR cannot be reduced further more than a few percent. Also, CVaR constraints can be handled efficiently using equivalent linear constraints, which dramatically improves the efficiency of the optimization techniques.