The dependence of the carrier velocity on the width of energy (diagonal) disorder for a model of amorphous solids is analysed using a numerical simulation technique. In contrast with the behaviour in the low-driving-field region where the carrier velocity always decreases with increasing disorder, for high bias fields, the presence of small amounts of disorder induces non-monotonic behaviour, showing a maximum of the carrier velocity at non-zero disorder strength. A discussion of this phenomenon in terms of the distribution of jumps in the three spatial directions of the system is carried out. Some evidence suggesting that this behaviour might occur in real materials is presented.