This study evaluates the efficiency of cross hedging with single stock futures (SSF) contracts. We propose a new technique for hedging exposure to an individual stock that does not have options or exchange-traded SSF contracts written on it. Our method selects as a hedging instrument a portfolio of SSF contracts which are selected based on how closely matched their underlying firm characteristics are with the characteristics of the individual stock we are attempting to hedge. We investigate whether using cross-sectional characteristics to construct our hedge can provide hedging efficiency gains over that of constructing the hedge based on return correlations alone. Overall, we find that the best hedging performance is achieved through a portfolio that is hedged with market index futures and a SSF matched by both historical return correlation and cross-sectional matching characteristics. We also find it preferable to retain the chosen SSF contracts for the whole out-of-sample period while re-estimating the optimal hedge ratio at each rolling window.