Multiple Description Coding (MDC) techniques have been explored in recent years as an alternative to other methods to provide robustness to multimedia information in the presence of losses. In a MDC approach some redundancy is preserved in the source coding so that, after appropriate packetization, if packet losses occur it is possible to recover by exploiting the redundancy (statistical or deterministic) between what was received and what was lost. While MDC techniques have shown some promising results, one potential drawback is the fact that changing their redundancy level may entail significant changes to the system. Since the level of redundancy should be adjusted to match the specific channel conditions, the difficulty in adapting can be a significant problem for time varying transmission scenarios. As an example, MDC techniques based on transform coding would require a modification of the transform at encoder and decoder each time the channel conditions change. In our previous work, we have proposed a simple approach for MDC that involves using a polyphase transform and deterministic redundancy (e.g., each sample of input data is transmitted several times, with different coding rates). This approach is useful in that it greatly simplifies the design of a MDC scheme, since the rate allocation determines the amount of redundancy. Moreover, it provides a great deal of flexibility as it enables the choice of redundancy to be almost arbitrary. To demonstrate the effectiveness of our system we introduce an optimal bit allocation algorithm that allows us to select the amount of redundancy to be introduced in the signal that best matches a given target packet loss rate. It is clear that such a trade- off exists, as the level of redundancy should increase when the packet loss rate increases, at the cost of some degradation in the corresponding error free performance. Our results show significant differences between optimal and suboptimal choices of redundancy. Moreover, given that the decoder remains unchanged when the bit allocation changes it is possible to adapt very simply to the changes in channel behavior without requiring a change in the packet sizes, or the structure of the decoder.