A series of (InAs) m (GaAs) n short-period superlattice layers with m = 0.87, 1, 1.15, or 2 and n = 3, 5, 6, 7, or 8 were grown about 0.3-mu-m thick on GaAs substrates by migration enhanced epitaxy. Changes in reflection high-energy electron diffraction (RHEED) patterns indicate that the surface is roughened by InAs layers, but becomes smooth by deposition of GaAs layers. Large or nonintegral m induces more surface roughening, while large n is more effective in smoothing. For most samples, RHEED patterns became spotty beyond some total superlattice thickness depending on m and n. The positions and full width at half-maximums of the zeroth-order superlattice peaks of x-ray diffraction are correlated to the observations in RHEED. We conclude that strain-induced interface roughening is one of the major causes to short-period superlattice imperfections, and that nonintegral InAs layers significantly affect the roughening.