A difficulty sometimes encountered in least-squares fitting of a one-compartment model with first-order absorption is that estimated values (ka and ke) of the rate constants of absorption and elimination are almost identical, are highly correlated and have very large standard deviations. This anomaly is explained by the existence of a class of data sets for which least-squares estimates of the rate constants are complex quantities. Such data sets may arise either from an unfortunate combination of random (e.g. assay) errors in the concentration values if ka and ke are sufficiently similar in magnitude, or from delayed absorption.