Summary: Let \(T\) be a tree. The reducible stem of \(T\) is the smallest subtree that contains all branch vertices of \(T\). In this paper, we first use a new technique of R. J. Gould and W. Shull [Discrete Math. 343, No. 1, Article ID 111581, 7 p. (2020; Zbl 1429.05040)] to state a new short proof for a result of M. Kano et al. [Ars Comb. 103, 137–154 (2012; Zbl 1265.05100)] on the spanning tree with a bounded number of leaves in a claw-free graph. After that, we use a similar idea to prove a sharp sufficient condition for a claw-free graph having a spanning tree whose reducible stem has few leaves.