We have studied the role of a low-viscosity zone in the uppermost mantle on convective instabilities in the cooling oceanic plates. The upper mantle is represented by three layers in a finite element model: a conducting lid overlies a low-viscosity zone, which in turn overlies a layer of constant viscosity extending to the base of the upper mantle (at 675 km in depth). The viscosity contrast, the Rayleigh number, the relative fluid layer thicknesses, and the conducting lid thickness are varied. If the Rayleigh number of the low-viscosity zone exceeds a critical value, then convection will be confined to the low-viscosity zone for a period which depends on the viscosity contrast and the Rayleigh number. However, the scale of the convection will eventually grow and extend throughout the upper mantle. We compare our model to the small-scale geoid and topography anomalies observed in the central Pacific, which are 50--80 cm in geoid and ~250 m in topography 10--40 m.y. after plate formation and whose wavelength (150--500 km) increases with age. The magnitude, early onset time, and lifetime of the anomalies suggest a viscosity contrast of greater than 2 orders of magnitude. The increase in wavelength with time also suggests a high Rayleigh number (≥106), and the initial 150--250 km wavelength indicates a low-viscosity zone thickness of 75--125 km. Small-scale convection does not alter the slope of the depth-age curve but does elevate the depth-age curve by ≥250 m. It is not until the onset of long-wavelength convection that the depth-age curve departs from (age)1/2 predicted by a cooling half-space. These results agree with the depth-age behavior observed in the Pacific, where the depth-age curve is elevated in the region of small-scale anomalies and departs from (age)1/2 at 70 m.y. The models also predict heat flow values on old ocean floor which are higher than the plate model (50--55 mW/m2) but which are in agreement with heat flow measurements in the Atlantic and Pacific. ¿ American Geophysical Union 1988