Many digital communication channels are affected by errors that tend to occur in bursts. A great deal of work has been devoted to finding good burst-error-correcting codes and developing burst-error-correcting schemes. However, burst-error-correcting codes are generally not effective for long bursts. Some burst-error-correcting schemes suffer long delay in decoding. Others are very sensitive to random errors in the guard space. Most of these schemes are not adaptive to channel conditions. A new adaptive scheme is proposed to overcome these drawbacks. The scheme employs a combination of two complementary punctured convolutional (CPC) codes. One of the codes is used for burst detection and for channel state estimation, and both codes are used for error correction. The proposed scheme is analyzed over a two state Markov chain channel model. Unlike existing burst-error-correcting schemes, it is shown that the proposed scheme is adaptive to channel conditions and less sensitive to errors in the guard space. For the same delay, the proposed scheme offers better performance than the interleaving schemes. When the channel is heavily corrupted by bursts, the improvement is even more pronounced.