The sound radiation of 3-MHz acoustically driven air bubbles in liquid is analyzed with respect to possible applications in second harmonic ultrasound diagnostics devices, which have recently come into clinical use. In the forcing pressure amplitude Pa = 1–10 atm and ambient radius R0 = 0.5–5 µm parameter domain, a narrow regime around the resonance radius R0 ~ 1–1.5 µm and relatively modest Pa ~ 2–2.5 atm is identified in which optimal sound yield in the second harmonic is achieved while maintaining spherical stability of the bubble. For smaller Pa and larger R0 hardly any sound is radiated; for larger Pa bubbles become unstable toward nonspherical shape oscillations of their surface. The computation of these instabilities is essential for the evaluation of the optimal parameter regime. A region of slightly smaller R0 and Pa ~ 1–3 atm is best suited to achieve large ratios of the second harmonic to the fundamental intensity. Spherical stability is guaranteed in the suggested regimes for liquids with an enhanced viscosity compared to water, such as blood.