Residual total magnetic field anomalies, relative to the best fitting uniform magnetization models, are large and spatially coherent over three small Tertiary seamounts on the Cocos plate. Furthermore, the paleomagnetic parameters determined from the uniform magnetization models in some cases disagree significantly with those predicted from models of absolute motion for the Cocos plate. Inversion of the sea surface magnetic anomaly using a least squares procedure which allows magnetization to vary among different sections of each seamount shows clear polarity reversals in two of the seamounts studied. The reversed zones constitute about 10% of the seamount volume. For the third seamount the nonuniform magnetization solution more correctly determines the paleomagnetic inclination and declination for the only section of the dipolar anomaly not obscured by a magnetic lineation traversing the area. The polarities indicated in the least squares solutions were confirmed by magnetic gradiometer measurements from the submersible Alvin. For all three seamounts the paleomagnetic latitudes and/or rotation angles in the nonuniform magnetization solutions changed appreciably (by as much as 20¿) to agree better with plate motion models. The nonuniform magnetization models reveal that growth rates for such volcanoes approach 1000 km3/Ma, with the final phase of volcanism consisting of summit, as opposed to flank, eruptions. The largest of the three volcanoes formed off-ridge on lithosphere at least 0.5 Ma old and may have remained active for 1 Ma. Hydrothermal activity apparently persists at least 0.7 Ma after the last major phase of volcanism.