Two experiments were recently reported describing the control of autonomous oscillatory chemical systems in the chaotic regime. Petrov, Gáspár, Masere, and Showalter[1] stabilized periodic orbits in the Belousov-Zhabotinsky reaction and we recently reported[2] the first experiment to control chaotic oscillations in an electrochemical cell. In controlling the electrochemical cell we found it necessary, in general, to use the recursive proportional-feedback (RPF) algorithm recently developed by Rollins, Parmananda, and Sherard[3]. The RPF algorithm is simple to apply and is generally applicable to highly dissipative systems that are well described by a one-dimensional Poincaré return map of a single measured variable. In this paper we report the further use of the RPF algorithm to stabilize both period-1 and period-2 orbits in the electrochemical system. We also present experimental evidence that suggests why we found it necessary to use the new RPF method instead of the simple proportional feedback method suggested by Petrov, Peng, and Showalter[4] and by Hunt[5] that often works for systems well described by a one-dimensional return map. Finally, we briefly discuss the robustness of the RPF method. This discussion is based on an analysis of the RPF method in terms more akin to standard control theory[6] as described recently for the general high dimensional system by Romeiras, Grebogi, Ott, and Dayawansa[7]. This approach treats the experimental system (described by a one-dimensional return map of a single variable) together with a linear recursive control stratagy applied to a single control parameter as a discrete two-dimensional system. The desired periodic orbit is a fixed point of the two-dimensional map. The range of acceptable control conditions is determined by the requirement that the fixed point remain stable. The RPF control stratagy[3] makes the fixed point superstable.