We derive explicit approximations for variance-optimal hedging strategies in the lognormal SABR and in the rough Bergomi model. In the SABR model the approximately variance-optimal (AVO) strategy coincides with the Delta adjustment proposed earlier by Bartlett. We analyze — both analytically and in simulation — the mean-square hedging error of the AVO strategy in comparison to delta hedging and discuss its dependency on the leverage parameter rho and on the Hurst exponent controlling the roughness of the model.