Abrupt interfaces between ZnMgO and ZnO are strained due to lattice mismatch. This strain is relaxed if there is a gradual incorporation of Mg during growth, resulting in a diffuse interface. This strain relaxation is however accompanied by reduced confinement and enhanced Mg-ion scattering of the confined electrons at the interface. Here we experimentally study the electronic transport properties of the diffuse heteroepitaxial interface between single-crystal ZnO and ZnMgO films grown by molecular-beam epitaxy. The spatial extent of the interface region is controlled during growth by varying the zinc flux. We show that, as the spatial extent of the graded interface is reduced, the enhancement of electron mobility due to electron confinement more than compensates for any suppression of mobility due to increased strain. Furthermore, we determine the extent to which scattering of impurities in the ZnO substrate limits the electron mobility in diffuse ZnMgO–ZnO interfaces.