The Chandler wobble frequency F and quality factor Q are estimated by least squares using polar motion data in combination with proxy excitations derived from atmospheric data. Monte Carlo tests show that this approach can provide useful improvements over traditional maximum likelihood methods, which use only observed polar motion. With less than a decade of good simultaneous polar motion and atmospheric data there is no new information about Q, but 90% confidence intervals for F are near ¿0.004 cycles per year (cpy), making them comparable to maximum likelihood results based on nearly a century of historical polar motion data. Using our preferred proxy excitation, we obtain an estimate of F near 0.831 cpy (a period of 439.5 mean solar days), which is significantly different from the maximum likelihood value near 0.843 cpy (433 days). This difference can be understood in light of differences in assumptions underlying the two methods. ¿ American Geophysical Union 1996