The nature and origin of lateral composition modulations in (AlAs)m(InAs)n short-period strained-layer superlattices grown by molecular beam epitaxy on InP substrates have been investigated by x-ray diffraction, atomic force microscopy, and transmission electron microscopy. Strong modulations were observed for growth temperatures between ≈ 540 and 560° C. The maximum strength of modulations was found for SPS samples with InAs mole fraction x (= n/(n+m)) close to ≈ 0.50 and when n ≈ m ≈ 2. The modulations were suppressed at both high and low values of x. For x > 0.52 (global compression), the modulations were along the <100> directions in the (001) growth plane. For x < 0.52 (global tension), the modulations were along the two <310> directions rotated ≈ ±27° from  in the growth plane. The remarkably constant wavelength of the modulations, between ≈ 20–30 nm, and the different modulation directions observed, suggest that the origin of the modulations is due to surface roughening associated with the high misfit between the individual SPS layers and the InP substrate. Highly uniform unidirectional modulations have been grown by control of the InAs mole fraction and growth on suitably offcut substrates, which show great promise for application in device structures.