Rao, Hartley and Cochran's (HRC) estimator of a survey population total is known to be a competitor against Horvitz and Thompson's. The generalized regression estimator as an adjustment on the latter is known to yield appreciable gain in efficiency if the regression of the variable of interest on a correlated variable with known population values is a straight line through the origin. We empirically investigate through simulations on live data how effective corresponding regression adjustment on the RHC estimator may be. The exercise is extended to cover sensitive issues for which instead of direct responses only randomized responses are available. The numerical exercise seems illuminating.