In this paper, we consider distributed multimedia processing on wirelessly networked handheld devices, where multimedia data are heavily processed when transferred between the server and the handheld. We show that, to minimize battery consumption on the handheld, a tradeoff often needs to be made between the energy consumed by computation versus that by data transfer. We develop an energy cost model and present a task partition and allocation scheme to divide the data-processing responsibility between the server and the handheld. Experiments are performed on a Compaq iPAQ device which is connected to a server via a WaveLan interface. Out of 17 programs from the Mediabench suite, our scheme is shown to save energy significantly in 13 of them over the default mode of processing data locally on the handheld.