Traditionally, research into self-assembled quantum dots (SAQDs) has focused on compressively strained materials on (001) substrates. Nevertheless, SAQDs on other low-index surfaces may have attractive properties; long spin-lifetimes and a lack of fine-structure splitting are associated with heterostructures on (110) and (111) substrates respectively. SAQDs on (110) and (111) surfaces could therefore be useful for spintronics and quantum optics. However, compressively strained materials typically form relaxed 2D layers on (110) and (111) surfaces, due to the preferential glide of 90° partial dislocations.[1,2] By focusing instead on tensile strained materials, we demonstrate that it is possible to grow self-assembled GaP islands on both GaAs(110) and (111)A surfaces. Our results are consistent with the Kvam-Hull strain relaxation model in which the combination of tensile strain <I>and</I> (110) or (111) surfaces prohibits the glide of 90° partial dislocations. Moreover, nucleation of allowed 60° dislocations is kinetically limited; strain relief thus occurs by the observed self-assembly of dislocation-free, 3D islands. We have previously reported the spontaneous formation of 3D GaP islands at step-edges on GaAs(110) buffers. Island growth proceeds without a wetting layer, consistent with the Volmer-Weber (VW) mechanism. These dislocation-free GaP islands exhibit monomodal size distributions, which are tunable with GaP thickness. Adatom diffusion length on GaAs(110) is large and equivalent to buffer terrace widths. As a result, GaAs(110) step-edges mediate island nucleation, even at deposition thicknesses << 1 ML. This presentation focuses on results obtained for tensile growth on (111) surfaces. MBE of GaP/GaAs(111)A leads to uniform self-assembled 3D islands, albeit with many differences from those formed on (110) surfaces. Given the relative surface energies of GaP(111)A and GaAs(111)A we predicted VW growth, and this was confirmed by submonolayer island nucleation. We demonstrate that island size and density are controllable as a function of both growth temperature and GaP thickness. Cross-sectional and plan-view transmission electron microscopy show that tensile GaP/GaAs(111)A islands are dislocation-free. We speculate that some of the differences in growth behavior between GaP/GaAs(110) and GaP/GaAs(111)A may result from the shorter adatom diffusion length on GaAs(111)A. GaP/GaAs(111)A island size scales for GaP deposition between 0.17 and 1.73 ML. Fitting our scaled island size distributions with functions of the form derived by Amar and Family, we obtain a critical island size for GaP/GaAs(111)A of 1–3 adatoms. By applying our understanding of GaP/GaAs island formation to tensile systems offering quantum confinement, we hope in the future to realize SAQDs on (110) and (111)A surfaces.