  This paper proves that in any closed Riemannian surface $M$ with diameter
$d$, the length of the $k^\text{th}$-shortest geodesic between two given points
$p$ and $q$ is at most $8kd$. This bound can be tightened further to $6kd$ if
$p = q$. This improves prior estimates by A. Nabutovsky and R. Rotman.
