Lattice-mismatched epitaxy produces a high concentration of dislocations (N-dis) in the interface region, and this region is often highly conductive, due to donor (N-D) decoration of the dislocations. Here we show that a simple postulate, N-D = alpha (N-dis/c), where c is the lattice constant and alpha a constant of order 1-2, predicts a nearly constant low-temperature mobility, independent of N-dis This prediction is experimentally verified in GaN grown on Al2O3, and is also applied to other mismatched systems. (C) 2001 Elsevier Science Ltd. All rights reserved.