  Let $T$ be a tree, a vertex of degree one is a \emph{leaf} of $T$ and a
vertex of degree at least three is a \emph{branch vertex} of $T$. The {\it
reducible stem } of $T$ is the smallest subtree that contains all branch
vertices of $T$. In this paper, we give some sharp sufficient conditions for
$K_{1,4}$-free graphs to have a spanning tree whose reducible stem having few
leaves.
