  We make a proposal for incorporating massless modes into the spin-chain of
the AdS3/CFT2 integrable system. We do this by considering the alpha to 0 limit
of the alternating d(2,1;alpha)^2 spin-chain constructed in arXiv:1106.2558. In
the process we encounter integrable spin-chains with non-irreducible
representations at some of their sites. We investigate their properties and
construct their R-matrices in terms of Yangians.
