We consider two capture-recapture models that imply that the logit of the probability of capture is an additive function of an animal catchability parameter and a parameter reflecting the sampling effort. The models are special cases of the Rasch model, and satisfy the property of quasi-symmetry. One model is log-linear and the other is a latent class model. For the log-linear model, point and interval estimates of the population size are easily obtained using standard software, such as GLIM.