  In the Steiner point removal (SPR) problem, we are given a weighted graph
$G=(V,E)$ and a set of terminals $K\subset V$ of size $k$. The objective is to
find a minor $M$ of $G$ with only the terminals as its vertex set, such that
the distance between the terminals will be preserved up to a small
multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a
ball-growing algorithm with exponential distributions to show that the
distortion is at most $O(\log^5 k)$. Cheung [Che17] improved the analysis of
the same algorithm, bounding the distortion by $O(\log^2 k)$. We improve the
analysis of this ball-growing algorithm even further, bounding the distortion
by $O(\log k)$.
