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This paper studies the possibility of implementing Pareto optimal outcomes in the combinatorial auction setting where bidders may have budget constraints. I show that when the setting involves a single good, or multiple goods but with single‐minded bidders, there is a unique mechanism, called truncation Vickrey–Clarke–Groves (VCG), that is individually rational, incentive compatible, and Pareto optimal. Truncation VCG works by first truncating valuations at budgets, and then implementing standard VCG on the truncated valuations. I also provide maximal domain results, characterizing when it is possible to implement Pareto optimal outcomes and, if so, providing an implementing mechanism. Whenever there is at least one multi‐minded constrained bidder and another multi‐minded bidder, implementation is impossible. For any other domain, however, implementation is possible.