A scheme is presented for the reduction of threading dislocation densities in InxGa1−xAs/GaAs epitaxial single layers by accurate control of layer thickness. The model developed differs from previous models since the InxGa1−xAs growth is restricted to less than ten times the Matthews and Blakeslee critical thickness (hc) where the asymmetry in the [110] and [1¯10] dislocation densities is the greatest. Beyond this thickness it is shown that the removal or annihilation of threading dislocations in the epilayer is more than offset by the introduction of new threading dislocations from spiral and Frank–Read‐type sources. Maintaining epilayer thickness below this thickness ensures that the majority of misfit dislocations generated lie predominantly in only one of the ⟨110⟩ directions, reducing the likelihood of blocking with orthogonal dislocations, thereby increasing the mean free path from that expected in higher density dislocation arrays. Etch pit densities show that the threading dislocation density can be reduced by up to a factor of 10 below that found in the substrate, with the added benefit of reducing the inhomogenities in the distribution of threading dislocations. Atomic force microscopy shows that the surface quality of these layers remains high with an absence of striations. ©1996 American Institute of Physics.