A simplification of the well known stochastic iteration algorithm, called the dual sign algorithm (DSA), has been proposed recently for adaptive identification and similar applications. There are two key parameters that must be determined for the efficient use of the algorithm, namely the quantisation levelL2and the thresholdrT. Whereas there exists a simple method for the design of these parameters, in the present paper an optimal design theory is developed by studying the relationship betweenL2and the convergence rate. It is found that there is no simple way to obtain a best value ofrTfor the optimally chosenL2value. Instead, a modification of the DSA is proposed that realises the optimum performance suggested by the theory. Computer simulation is used to support the theoretical results.