We compare the influence of different mechanisms for driving convection in the Earth's core on the structure of the magnetic and velocity fields using a 3D numerical dynamo model. We find dynamos with a dipolar magnetic field in cases of chemical convection or convection driven by an imposed temperature contrast. With purely internal heating we obtain only dynamos with a quadrupolar or more complex field. The relative strength of convection and magnetic field generation in the regions close to the poles depends on whether a condition of fixed composition or of fixed chemical flux is specified on the inner core boundary. If applicable to the geodynamo, our results favor the dominance of chemical convection during the past 3 Gyr. ¿ 2000 American Geophysical Union