A weighted martingale method, akin to a moving average, is proposed to allow the use of modified closed-population methods in the estimation of the size of a smoothly changing open population when there are frequent capture occasions. We concentrate here on modifications to martingale estimating functions for model Mt, but a wide range of closed-population estimators may be modified in this fashion. The method is motivated by and applied to weekly capture-recapture data from the Mai Po bird sanctuary in Hong Kong. Simulations show that the weighted martingale estimator compared well with the Jolly-Seber estimator when the conditions for the latter to be valid are met, and it performed far better when individuals were allowed to leave and reenter the population. Expressions are derived for the asymptotic bias and variance of the estimator in an appendix.