Models of the tidally heated, floating ice shell proposed for the jovian satellite Europa generally find shell thicknesses less than 30 km. Past parameterized convection models indicated that such shells are stable against convective overturn, which otherwise ostensibly leads to freezing of the ocean underneath. Here I apply the temperature-dependent viscosity convection scaling developed by Solomatov and coworkers to the Europan ice shell. The temperature-dependent properties of ice are linearized about 260 K, as any convective interior should be close to this temperature, with the colder ice forming an essentially passive, stagnant lid. Ice shells ≥10 km thick are found to be unstable to convection at their base for melting-point viscosities of 1013 Pa-s (as linearized by tidal stresses), if the ice deforms by superplastic creep, but such low viscosities require small grain sizes (<1 mm). This requirement may be met if grain sizes observed in terrestrial polar glaciers can be strain-rate scaled to Europa. Regardless, convection at the base of the ice shell, if initiated, may not freeze the ocean. Because of tidal heating, a stagnant-lid regime ice shell is much more dissipative than a conductive shell of the same thickness. Such a shell should thin, not thicken, and the potential exists for further thermal instabilities and runaways. ¿ 1999 American Geophysical Union