Abstract: The "slow-coloring game" is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the remaining vertices, scoring $|M|$ points. Painter then deletes a subset of $M$ that is independent in $G$. The game ends when all vertices are deleted. Painter's goal is to minimize the total score; Lister seeks to maximize it. The score that each player can guarantee doing no worse than is the "slow-color cost" of $G$, written $s(G)$. The game is a variant of online list coloring. We have obtained the following results. Trivially lower and upper bounds on $s(G)$ are the chromatic sum and the sum-paintability, with equality in the lower bound when $\alpha(G)\le2$ and equality in the upper bound if and only if all components are complete (the "chromatic sum" is the minimum sum of vertex colors in a proper coloring by positive integers). We give sharp upper and lower bounds on $s(G)$ in terms of the independence number. Among $n$-vertex trees, $s(G)$ is minimized by the star and maximized by the path (where it equals $3n/2$). We give good bounds on $s(K_{r,s})$. These results are joint with Thomas Mahoney and Gregory Puleo. We will also discuss a later linear-time algorithm to compute $s(G)$ exactly when $G$ is a tree, which is joint work with Gregory Puleo.