We propose a new Nakagami phase-envelope fading channel simulator that (i) allows for arbitrary real values of fading parameter, (ii) exactly matches the Nakagami first-order statistics, (iii) and closely matches the second-order statistics classically assigned to Nakagami fading. The proposed simulator is based on a cascade of two existing simulators-the random-mixture simulator and the rank-matching simulator. It combines the strenghts of these two simulators, outperforming them both.12523232333