We present a series of results providing evidence that the incentive problem with VCG-based mechanisms is not very severe. Our first result uses average-case analysis to show that if an algorithm can solve the allocation problem well for a large proportion of instances, incentives to lie essentially disappear. We next show that even if such incentives exist, a simple enhancement of the mechanism makes it unlikely that any player will find an improving deviation. In the experimental part of the paper, we demonstrate that incentives to lie decrease with increasing problem complexity. However, we also note that if incentives to lie do exist, they can have a negative impact on welfare.