In this paper aberrations in Alvarez-Lohmann lenses are analyzed, and a semi-analytical strategy for compensation is derived. An x-y polynomial model is used to describe the aberrations and classify them into static and dynamic components. The lenses are enhanced by higher-order polynomials, and a numerical optimization process is used to determine the most influential coefficients. Two simulations of corrected systems are presented. The first one is optimized for on-axis imaging. The second system is optimized for multiple field points and shows the limitations of a single Alvarez-Lohmann lens. Two systems overcoming these limitations by introducing additional optical surfaces are presented, and their performance is analyzed in simulations.