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Several experimental studies in the literature have investigated how time preferences govern bargaining outcomes in the canonical, infinite-horizon, alternating-offers bargaining model of Rubinstein (1982), but the evidence is mixed. We revisit the problem with a novel experimental design in which bargaining game payoffs are paid over a long period of time with different payment windows (weekly or monthly) exogenously assigned to each subject. Using this effective discounting procedure, we test the theoretical predictions presented 1) in the absence of dynamically inconsistent time preferences (Rubinstein, 1982) and 2) in the presence of such time-inconsistent preferences (Schweighofer-Kodritsch, 2018). We find unambiguous experimental support for several major theoretical predictions. In all treatments, the vast majority of agreements were reached with no or minor delays and with a significant and substantial first-mover advantage. In the treatment without any delayed (1 week) payment schedule, the bargainer with a larger effective discount factor received a significantly larger share. In the treatment in which immediate agreement was made impossible by a payment delay introduced to both bargainers, however, the difference in the agreed-upon shares between the bargainers with different effective discount factors became less significant statistically and less substantial in magnitude. These results suggest that bargainers’ discount function exhibits diminishing impatience after failing to reach an immediate agreement.