A unified approach is suggested to estimate the population size for a closed population in discrete time. Individuals can be removed after capture at any time during the experiment. The usual recapture and removal experiments are shown to be particular cases of the general formulation. The capture probability is assumed to have a logistic function that depends on individual covariates and can be time dependent. The unified approach involves a two-step procedure. A conditional likelihood function is used to estimate the covariates' coefficients and a Horvitz-Thompson type estimator to estimate the population size. The asymptotic and small-sample properties of the resulting estimators are investigated. A real example is given.