In a capture–recapture experiment, the number of measurements for individual covariates usually equals the number of captures. This creates a heteroscedastic measurement error problem and the usual surrogate condition does not hold in the context of a measurement error model. This study adopts a small measurement error assumption to approximate the conventional estimating functions and the population size estimator. This study also investigates the biases of the resulting estimators. In addition, modifications for two common approximation methods, regression calibration and simulation extrapolation, to accommodate heteroscedastic measurement error are also discussed. These estimation methods are examined through simulations and illustrated by analysing a capture–recapture data set.