In the context of entry-level labor markets, we consider the potential transactions that have to be evaluated before equilibrium transactions can he identified. These potential transactions involve offers that are rejected. After an initial phase in which many offers can be proffered in parallel, subsequent potential transactions must be processed serially, since a new offer cannot be made until an outstanding offer is rejected. In this phase even a small time required to process offers and rejections may cause bottlenecks. In many, perhaps most, decentralized labor markets, this means that transactions have to be finalized before there is time for the market to clear, that is, before all the potential transactions that would need to be evaluated in order to reach a stable outcome can in fact be evaluated. This has implications for the strategic behavior of firms and workers. In particular, in deciding to whom to offer a position, a firm may have strong incentives to consider not only its preferences over workers but also the likelihood that its offer will be accepted, since if its offer is rejected it may find that many other potential employees have become unavailable in the interim. The analysis is carried out in connection with the decentralized market for clinical psychologists. The implications for other kinds of markets are considered.