  We study individual rational, Pareto optimal, and incentive compatible
mechanisms for auctions with heterogeneous items and budget limits. For
multi-dimensional valuations we show that there can be no deterministic
mechanism with these properties for divisible items. We use this to show that
there can also be no randomized mechanism that achieves this for either
divisible or indivisible items. For single-dimensional valuations we show that
there can be no deterministic mechanism with these properties for indivisible
items, but that there is a randomized mechanism that achieves this for either
divisible or indivisible items. The impossibility results hold for public
budgets, while the mechanism allows private budgets, which is in both cases the
harder variant to show. While all positive results are polynomial-time
algorithms, all negative results hold independent of complexity considerations.
