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We study the data dissemination problem in time-constrained mobile computing systems (TCMCS) in which maximizing data currency (minimizing staleness) and meeting transaction deadlines are of equal importance as providing consistent data items to transactions. We first investigate what are the performance problems of the multi-version data (MV) broadcast technique when it is used for TCMCS. Then, we propose various enhancements to resolve the problems. In order to further reduce the probability of missing deadlines, we introduce a prioritized on-demand broadcast scheme, which is integrated with the data broadcast mechanism for disseminating data items to time-constrained transactions. The performance characteristics of the proposed strategies have been studied through extensive simulation.