  It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms
in multidimensional type spaces may involve randomization. We obtain conditions
under which deterministic mechanisms are optimal for selling two identical,
indivisible objects to a single buyer. We analyze two settings: (i) decreasing
marginal values (DMV) and (ii) increasing marginal values (IMV). Thus, the
values of the buyer for the two units are not independent.
  We show that under a well-known condition on distributions~(due to McAfee and
McMillan (1988)), (a) it is optimal to sell the first unit deterministically in
the DMV model and (b) it is optimal to bundle (which is a deterministic
mechanism) in the IMV model. Under a stronger sufficient condition on
distributions, a deterministic mechanism is optimal in the DMV model.
  Our results apply to heterogeneous objects when there is a specified sequence
in which the two objects must be sold.
