While the Almost Ideal Demand System (AIDS) has received increasing attention in empirical studies of consumer demand, the fact that the underlying PIGLOG cost function is not globally regular has often led to violation of negative semi-definiteness in the estimated Slutsky matrix. This paper suggests a modification to the PIGLOG class of preferences, termed MPIGLOG, which preserves regularity in a wider region of expenditure- price space. In an empirical section the AIDS special case of PIGLOG is compared with the analogous special case of MPIGLOG, which we term MAIDS. The comparison demonstrates the improved regularity features of MAIDS.