A variation of the usual semiclassical short wavelength (eikonal) method was recently applied to model calculations of electronically diabatic atom–atom collisions. Microreversibility was computationally imposed on the dynamics by following trajectories initiating in the ground and excited states simultaneously. When imporved transition probabilities for several two-state systems were obtained in this manner, a multistate application was selected. Self-consistent eikonal/averaged effective potential (SCE/AEP) state to state calculations are performed for rotationally inelastic HeH2 scattering at total energies of .1 and .9 eV. using an (8,2) basis (7 states). Phase shifted amplitudes are introduced that add constraints to the coupled differential equations and reduce cpu time. Definite parity partial and total cross sections compare favorably to the previous semiclassical coupled states (SCS) results of Billing (1978) as well as to both the quantum ADPjz and CC results of Shimoni and Kouri (1977). © 1993 John Wiley & Sons, Inc.