  Given a minor-closed class $\mathcal{A}$ of graphs, let $\beta_{\mathcal{A}}$
denote the supremum over all graphs in $\mathcal{A}$ of the ratio of edges to
vertices. We investigate the set $B$ of all such values $\beta_{\mathcal{A}}$,
taking further the project begun by Eppstein. Amongst other results, we
determine the small values in $B$ (those up to 2); we show that $B$ is
`asymptotically dense'; and we answer some questions posed by Eppstein.
