  We study the complexity of valued constraint satisfaction problems (VCSP). A
problem from VCSP is characterised by a \emph{constraint language}, a fixed set
of cost functions 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 consider the case of so-called \emph{conservative} languages; that is,
languages containing all unary cost functions, thus allowing arbitrary
restrictions on the domains of the variables. We prove a Schaefer-like
dichotomy theorem for this case: if all cost functions in the language satisfy
a certain condition (specified by a complementary combination of \emph{STP and
MJN multimorphisms}) then any instance can be solved in polynomial time by the
algorithm of Kolmogorov and Zivny (arXiv:1008.3104v1), otherwise the language
is NP-hard. This generalises recent results of Takhanov (STACS'10) who
considered $\{0,\infty\}$-valued languages containing additionally all
finite-valued unary cost functions, and Kolmogorov and Zivny
(arXiv:1008.1555v1) who considered \emph{finite-valued} conservative languages.
