The paper deals with distributions of spectroscopic line widths of single molecules as measured in disordered solids at low temperatures. The influence of the random orientation of the dye molecules and, hence, of the different amount of power broadening on the fluorescence excitation spectra is investigated. The resulting line width distributions are calculated as a function of laser intensity and of the detection efficiency of the apparatus. It turns out that, for linearly polarized laser light, power broadening tends to give rise to asymmetric distributions that have a steep dope at narrow widths and a longer tail at broad widths. Possible implications for experimental line width histograms are discussed.