  For two graphs, $G$, and $H$, an edge-coloring of a complete graph is
$(G,H)$-good if there is no monochromatic subgraph isomorphic to $G$ and no
rainbow subgraph isomorphic to $H$ in this coloring. The set of number of
colors used by some $(G,H)$-colorings of $K_n$ is called a mixed-Ramsey
spectrum. This note addresses a fundamental question of whether the spectrum is
an interval. It is shown that the answer is "yes" if $G$ is not a star and $H$
does not contain a pendent edge.
