We report on results from the first solar Fitting at Low-Angular degree Group (solar FLAG) hare-and-hounds exercise. The group is concerned with the development of methods for extracting the parameters of low-l solar p-mode data (`peak bagging'), collected by Sun-as-a-star observations. Accurate and precise estimation of the fundamental parameters of the p modes is a vital pre-requisite of all subsequent studies. Nine members of the FLAG (the `hounds') fitted an artificial 3456-d data set. The data set was made by the `hare' (WJC) to simulate full-disc Doppler velocity observations of the Sun. The rotational frequency splittings of the l = 1, 2 and 3 modes were the first parameter estimates chosen for scrutiny. Significant differences were uncovered at l = 2 and 3 between the fitted splittings of the hounds. Evidence is presented that suggests this unwanted bias had its origins in several effects. The most important came from the different way in which the hounds modelled the visibility ratio of the different rotationally split components. Our results suggest that accurate modelling of the ratios is vital to avoid the introduction of significant bias in the estimated splittings. This is of importance not only for studies of the Sun, but also of the solar analogues that will be targets for asteroseismic campaigns. Solar FLAG URL: http://bison.ph.bham.ac.uk/~wjc/Research/FLAG.html E-mail: wjc [at] bison.ph.bham.ac.uk (wjc[at]bison[dot]ph[dot]bham[dot]ac[dot]uk) ‡ George Isaak passed away in 2005 June 5, prior to the completion of this work. He is greatly missed by us all.