We consider the menu size of auctions and mechanisms in general as a measure of their complexity, and study how it affects revenue. Our setting has a single revenue-maximizing seller selling two or more heterogeneous goods to a single buyer whose private values for the goods are drawn from a (possibly correlated) known distribution, and whose valuation is additive over the goods. We show that the revenue may increase arbitrarily with menu size and that a bounded menu size cannot ensure any positive fraction of the optimal revenue. The menu size turns out also to “pin down” the revenue properties of deterministic mechanisms: their menu size is at most exponential in the number of goods, and indeed their revenue may be larger than that achievable by the simplest types of mechanisms by a similar factor.