  We study optimisation problems that can be formulated as valued constraint
satisfaction problems (VCSP). A problem from VCSP is characterised by a
\emph{constraint language}, a fixed set of cost functions taking finite and
infinite costs over a finite domain. An instance of the problem is specified by
a sum of cost functions from the language and the goal is to minimise the sum.
We are interested in \emph{tractable} constraint languages; that is, languages
that give rise to VCSP instances solvable in polynomial time. Cohen et al.
(AIJ'06) have shown that constraint languages that admit the MJN multimorphism
are tractable. Moreover, using a minimisation algorithm for submodular
functions, Cohen et al. (TCS'08) have shown that constraint languages that
admit an STP (symmetric tournament pair) multimorphism are tractable.
  We generalise these results by showing that languages admitting the MJN
multimorphism on a subdomain and an STP multimorphisms on the complement of the
subdomain are tractable. The algorithm is a reduction to the algorithm for
languages admitting an STP multimorphism.
