Classic direct mechanisms suffer from the drawback of requiring full type (or utility function) revelation from participating agents. In complex settings with multi-attribute utility, assessing utility functions can be very difficult, a problem addressed by recent work on preference elicitation. In this work we propose a framework for incremental, partial revelation mechanisms and study the use of minimax regret as an optimization criterion for allocation determination with type uncertainty. We examine the incentive properties of incremental mechanisms when minimax regret is used to determine allocations with no additional elicitation of payment information, and when additional payment information is obtained. We argue that elicitation effort can be focused simultaneously on reducing allocation and payment uncertainty.