We investigate the optimum transmission strategy that minimizes the overall distortion for delay-sensitive but distortion-tolerant data. We consider a set of source symbols residing at the transmitter that are encoded into a set of packets using multiresolution source coding. Each packet has a given deadline after which its transmission will be useless. Since multiresolution source codes are being used, the packet lengths can be adjusted by dropping less significant bits in order to allow for the more significant bits of a larger number of packets to be transmitted before the deadline. We find the optimum number of bits that must be transmitted of every packet to minimize the overall distortion when transmissions are error-free. We show that for strictly convex distortion functions the solution is unique and independent of the form of the function, and extend this result to the case where transmitted bits can be affected by noise and find the optimum strategy that leads to the minimum expected distortion. Finally we look at the case where packets arrive according to a given deterministic arrival schedule and present an algorithm that finds the optimum transmission strategy.