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 Kn 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.