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We consider applications of sensor networks wherein data packets generated by every node have to reach the base station. This results in a many-to-one communication paradigm referred to as convergecast. We are interested in determining a TDMA schedule that minimizes the total time required to complete the convergecast. We consider a simple version of the problem wherein every node generates exactly one packet. We propose a distributed convergecast scheduling algorithm that requires at most 3N timeslots, where N represents the number of nodes in the network. Through extensive simulations, we demonstrate that actual number of timeslots needed is around 1.5N. In addition to time efficiency, we prove that our convergecast scheduling algorithm requires the nodes to buffer no more than two packets at any instance. We propose a sleep schedule that conserves more than 50% of the energy. We present simulation results for a real application scenario to show that our convergecast scheduling algorithm performs significantly better than existing convergecast algorithms.