Phytoplankton maximum growth rate and the saturation light intensity, Is, can be estimated from vertical profiles of primary production by non-linear least-squares estimation. Solution through the normal equations leads to formulae which are relatively simple and easy to implement. The computation of confidence contours is demonstrated, and the results are contrasted to the confidence limits on the parameters individually. These can be quite misleading due to model non-linearity and correlation between parameter estimation. The procedure has been applied to primary production data from Lake Balaton, a shallow lake in Hungary. The growth rate-temperature relation is analysed by separating the parameters into two groups characteristic for “warm” and “cold” water phytoplankton, respectively. A bell-shaped curve is found for “cold” water communities, with an optimum at about 7–9°C, whereas the “warm” water phytoplankton exhibits a strong exponential dependency in the temperature range of interest (up to 25°C). Is also appears to be related to temperature except for the “cold” water group, where Is is essentially constant. However, a roughly linear relation with considerably less scatter is obtained when Is is plotted directly versus day-averaged solar radiation. This apparent fast adaptation is attributed to the extremely short turnover time in Lake Balaton. Maximum growth rates of 10–20 d−1 have been found for temperatures between 20 and 25°C. These results and a critical appraisal of available literature suggest that the common notion of maximum growth rates being in the order of 1–3 d−1 needs revision, at least for lakes with relatively high summer temperatures.