  It is shown that a trivial version of polarization is sufficient to produce
separating systems of polynomial invariants: if two points in the direct sum of
the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial
invariants, then they can be separated by invariants depending only on at most
$2\dim(V)$ variables of type $V$; when $G$ is reductive, invariants depending
only on at most $\dim(V)+1$ variables suffice. Similar result is valid for
rational invariants. Explicit bounds on the number of type $V$ variables in a
typical system of separating invariants are given for the binary polyhedral
groups, and this is applied to the invariant theory of binary forms.
