In tracer kinetic studies, two homogeneous well-mixed compartments may be related as precursor and product. The time constant for the product compartment can then be estimated from the two specific activity vs. time curves. We examine ten methods of estimating this time constant for data with several different error patterns, and conclude that the present practice of transforming the data to a straight line yields an inefficient but unbiased estimate of the time constant. A least squares estimate, appropriately weighted and taking into account that both precursor and product specific activities are subject to error is expected theoretically and found in practice, to be most efficient. It is however, mathematically complicated. A modified approach using a minimum χ2 estimate in which precursor specific activities are treated as error-free, is almost as efficient. It is mathematically simple, and outperforms the currently used estimators.