  We study the \emph{multiterminal cut} problem, which, given an $n$-vertex
graph whose edges are integer-weighted and a set of terminals, asks for a
partition of the vertex set such that each terminal is in a distinct part, and
the total weight of crossing edges is at most $k$. Our weapons shall be two
classical results known for decades: \emph{maximum volume minimum ($s,t$)-cuts}
by [Ford and Fulkerson, \emph{Flows in Networks}, 1962] and \emph{isolating
cuts} by [Dahlhaus et al., \emph{SIAM J. Comp.} 23(4):864-894, 1994]. We
sharpen these old weapons with the help of submodular functions, and apply them
to this problem, which enable us to design a more elaborated branching scheme
on deciding whether a non-terminal vertex is with a terminal or not. This
bounded search tree algorithm can be shown to run in $1.84^k\cdot n^{O(1)}$
time, thereby breaking the $2^k\cdot n^{O(1)}$ barrier. As a by-product, it
gives a $1.36^k\cdot n^{O(1)}$ time algorithm for $3$-terminal cut. The
preprocessing applied on non-terminal vertices might be of use for study of
this problem from other aspects.
