A model-reduction problem is considered which involves bothL2(quadratic) andH∞(worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize anL2model-reduction criterion subject to a prespecifiedH∞constraint on the model-reduction error. The principal result is a sufficient condition for characterizing reduced-order models with boundedL2andH∞approximation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e. idempotent matrix. When theH∞constraint is absent, the sufficient condition specializes to theL2model-reduction result given by Hyland and Bernstein (1985).