In radioimmunoassay and immunoradiometric assay, potency estimation involves the relation between counts of radioactivity and dose. Many workers have found the regression function to be satisfactorily represented by a logistic curve with limits that are themselves unknown parameters. This paper discusses estimation of all the parameters under the supposition (supported by empirical evidence) that the variance of a count is proportional to UJ, where U is the mean count at a dose and J is a parameter that almost certainly lies between 1.0 and 2.0. Estimation is found to be very robust, both in respect of the value taken for J and over alternative forms of least squares and maximum likelihood procedures. Special attention is given to whether the assay uses one or more doses of each test preparation, the former having important limitations but permitting some simplification of formulae. Requirements for a comprehensive computer program, suitable for routine use by assayists lacking statistical expertise and designed to produce potency estimates for a series of test preparations in one assay, are described. Data from an assay of oestradiol are used to illustrate various points.