Procurement auctions usually require the bid to specify several charac
teristics of the contract to be fulfilled. In this article I study the
design of such mechanisms, allowing for a special case of correlation
on the firm's costs. I describe the properties of optimal mechanisms
and study the design of multidimensional auctions. Contrary to the ind
ependent-costs model, to implement the optimal outcome the procurer wi
ll need to use a two-stage auction: in the first stage the procurer se
lects one firm; in the second stage he bargains to readjust the level
of quality to be provided.