This paper presents a general method for extracting solar cell parameters from current- voltage characteristics obtained under illumination. In particular, it focuses on the problem of measuring very low values of series resistance with sufficient precision. The method makes use of two different sets of experimental data: a cell current-voltage characteristic measured at a fixed sun irradiance level and a set of short circuit current and open circuit voltage value pairs measured at various sun irradiance levels. The method involves an interplay of different fitting procedures iteratively performed to these two data sets. The method is tested on two single junction silicon cells with the same very low series resistance however, having two very different values of shunt resistance. It is shown that in both cases this method is much more precise and reproducible than other conventional methods.