The low-temperature phase coexistence of size-asymmetric primitive model electrolyte solutions has been investigated by means of Monte Carlo simulations. A multidimensional parallel tempering method is employed and results are analyzed by means of histogram reweighting. Coexistence curves and critical constants are determined as a function of size asymmetry, lambda = sigma (+)/sigma (-), from 0.05 to 1. It is found that the critical temperature and the critical density decrease as lambda decreases. These trends appear to contradict available integral-equation theoretical predictions. For highly asymmetric systems, we report the formation of large chain-like and ring-like structures. These clusters are much larger than those observed in symmetric electrolytes, and they are shown to give rise to considerable finite-size effects. (C) 2001 American Institute of Physics.