The microstructure of spontaneous lateral composition modulation along the [110] direction has been studied in (InAs) n /(AlAs) m short-period superlattices grown by molecular beam epitaxy on (001) InP. X-ray diffraction and transmission electron microscopy show that global strain ( ) in the superlattice reduces the degree of composition modulation, which disappears for | |>0.7%. For tensile strains of ~+0.4%, we find that In-rich columns become regularly spaced and correlated with cusps in the growth surface. A similar correlation is seen in (InAs) n /(GaAs) m short-period superlattices between the enriched columns and the peaks and valleys of {114} A facets on the surface. The enriched columns in the (InAs) n /(GaAs) m layer (and the facets) extend for much longer distances (~0.2-0.4μm) in the [110] direction than do the columns in the (InAs) n /(AlAs) m layer (~56nm).