Many assembly systems are required to hold minimal work-in-process inventories because of space or capital limitations. Unfortunately, in the presence of variable processing times, output from an assembly line may be severely restricted if no work-in-process inventory is held. Thus, assembly lines often should be designed to have minimal, but not zero, buffer capacity. In this paper we address the issue of how one should optimally deploy limited buffer capacity in unbalanced assembly systems, and we find that the answer is sometimes counterintuitive. We study simple asynchronous assembly systems with random processing times and develop simple heuristic rules that can be used to improve existing operations and to support line designers who are faced with increasingly rapid cycles of new product introduction. We apply these heuristics to several larger systems and discover that they perform quite well.