The gains and reflectivities of the transverse-electric (TE) modes of GaAs large-cavity double-heterostructure (DH) (P-p-ń-N) lasers havebeen calculated in order to study mode selection perpendicular to the junction plane. The GaAs laser is modeled as a passive dielectric-slab waveguide composed of four layers whose optical constants are taken from recent literature. In lasers having a cavity thickness of a few microns, a small difference in refractive index between the p- and ń-region leads to the fundamental mode being confined to the p-region. Discrimination in favor of this mode without significant penalty in threshold gain may be achieved by utilizing the mode-dependent loss in the ń-layer. It is found that optimum mode discrimination in favor of the fundamental mode is governed by a suitable combination of the p-layer thickness, loss in the ń-region, and the difference of refractive indices of the p- and ń-layers. This analysis contrasts with an earlier analysis of the case of uniform refractive index in which it was found that the p-layer should be twice as thick as the n-layer for optimum mode discrimination. The calculated mode shapes in P-p-ń-N lasers are found to be in qualitative agreement with those observed recently by Hakki, and also with earlier observations that catastrophic mirror damage in P-p-ń-N lasers is confined to the p-region. Contrary to experimental observation, the model predicts that lasers having cavity thicknesses as large as 3 μm should operate stably in the fundamental mode. Possible reasons for this discrepancy are advanced. A simplification of the P-p-ń-N laser, which consists of omitting the N-layer thus yielding an asymmetric double-heterostructure laser, is suggested, and the merits and drawbacks of such a design are discussed.