In the model of high-field hopping studied extensively by Bassler and collaborators, disorder arising from the varying intersite wave function overlap (off-diagonal disorder) was incorporated by random assignment of an overlap decay rate to each site independently, admittedly an arguable procedure. We have carried out Monte Carlo simulations incorporating assignment of a random overlap to each bond. The assumptions of a Gaussian density of states and a Miller-Abrahams type of elementary jump rate were retained. We find the value and field variation of the mobility to be quite sensitive to the model of off-diagonal disorder considered. However, the results of our simulations may also be fitted by an exponential dependence of mobility on the square root of field for some ranges of field and parameters of the disorder.