This paper revisits the no-recall assumption in job search models with take-it-or-leave-it offers. Workers who can recall previously encountered potential employers, in order to engage them in Bertrand bidding, have a distinct advantage over workers without such attachments. Firms account for this difference when hiring a worker. When a worker first meets a firm, the firm offers the worker a sufficient share of the match rents to avoid a bidding war in the future. The pair share the gains to trade. In this case, the Diamond paradox no longer holds.