We present moderate-resolution (~50km/s FWHM) spectra of the Ly-alpha forest for seven quasars with redshifts ranging from 2.53 to 3.13, obtained with the Blue Spectrograph and photon-counting Reticon at the Multiple Mirror Telescope. Combined with spectra of 10 other quasars presented elsewhere, we have characterized the distribution of cloud properties in a way which was designed to minimize any subjective part of the analysis. We used artificial absorption spectra, with the same resolution, sampling and signal-to-noise ratio as a function of wavelength as the actual data. Distributions of the physical parameters of the Ly-alpha clouds, namely, the neutral hydrogen column density (N) and Doppler parameter (b), were approximated with d"N"/dN proportional to N^(-beta) and d"N"/db proportional to exp[-(b-)^2/(2 sigma_b^2)], respectively. We constructed a grid of simulated spectra with different input parameters. Comparison of properties of the simulated spectra with the observed spectra yielded acceptable ranges of parameters. Our technique differs from previous similar work in that we use the information contained in the distribution of the strength of the absorption in each resolution element and the distribution of separations between absorption complexes. We derive beta =1.4+/-0.1 for N ranging from 10^13 to 10^16cm^-2 and =30+/-15km/s. Most previous studies based on line lists indicated beta=1.7-1.9. We attribute this difference to flattening of the column density distribution for low N, recently confirmed by higher resolution observations. Our result for , though consistent with values quoted in the literature, is of lower significance, since it is less than the resolution of our spectra. We conclude by commenting on the importance of line blending in data sets of this kind.