It is widely believed that computing payments needed to induce truthful
bidding is somehow harder than simply computing the allocation. We show that
the opposite is true for single-parameter domains: creating a randomized
truthful mechanism is essentially as easy as a single call to a monotone
allocation function. Our main result is a general procedure to take a monotone
allocation rule and transform it (via a black-box reduction) into a randomized
mechanism that is truthful in expectation and individually rational for every
realization.