Calculations which improve upon the eikonal model description of the scattering of loosely bound n-cluster composite nuclei at low and medium energies are studied. Each cluster-target eikonal phase shift is replaced by the continuation of the corresponding exact partial wave phase shift to noninteger angular momenta. Comparisons with fully quantum mechanical calculations for two-body projectiles show that this yields an accurate practical alternative to few-body adiabatic model calculations. Calculations are shown to be accurate for projectile energies as low as 10 MeV/nucleon at which the eikonal approximation is no longer reliable.