  We recently proposed a new coding scheme for the L-channel multiple
descriptions (MD) problem for general sources and distortion measures involving
`Combinatorial Message Sharing' (CMS) [7] leading to a new achievable
rate-distortion region. Our objective in this paper is to establish that this
coding scheme strictly subsumes the most popular region for this problem due to
Venkataramani, Kramer and Goyal (VKG) [3]. In particular, we show that for a
binary symmetric source under Hamming distortion measure, the CMS scheme
provides a strictly larger region for all L>2. The principle of the CMS coding
scheme is to include a common message in every subset of the descriptions,
unlike the VKG scheme which sends a single common message in all the
descriptions. In essence, we show that allowing for a common codeword in every
subset of descriptions provides better freedom in coordinating the messages
which can be exploited constructively to achieve points outside the VKG region.
