In this paper, we study block codes that are optimized to recover some lost source data even in case when full recovery is not possible. Conventionally, block codes designed for packet erasure networks are aimed to recover all the lost source packets, assuming that the amount of lost data does not exceed the redundancy overhead. Unfortunately, this approach leads to poor performance if the fraction of lost data even occasionally exceeds the limit for full recovery capability. Recovery of part of the data may prove to be beneficial, especially when media data packets are unequal in importance. We present a short linear block code design that improves the performance of traditional Minimum Distance Separable (MDS) codes by reducing the fluctuation of the residual packet loss rate. These new codes also lead to a flexible design for unequal error protection of the media packets.