The sea-state bias in a satellite altimeter's range measurement is caused by the influence of ocean waves on the radar return pulse; it results in an estimate of sea level too low according to some function of the wave height. We have estimated this bias for Geosat by correlating collinear differences of altimetric sea-surface heights with collinear differences of significant wave heights (H1/3). Corrections for satellite orbit error are estimated simultaneously with the sea-state bias. Based on twenty 17-day repeat cycles of the Geosat Exact Repeat Mission, the solution for the sea-state bias is 2.6±0.2% of H1/3. The least-squares residuals, however, show a correlation with wind speed U, so we have supplemented the traditional model of the bias with a second term: α1H1/3+α2H1/3U. This second term produces a small, but statistically significant, reduction in variance of the residuals. Both systematic and random errors in H1/3 and U tend to bias the estimates of α1 and α2, which complicates comparisons of our results with ground-based measurements of the sea-state bias.