As part of a search for dust at high redshifts, we have acquired new spectra of quasars in the Wolfe et al. sample: 13 with damped Ly-alpha systems along the lines of sight and 15 without. Our spectra cover the region 3950-6900 angstrom at a resolution of 15 angstrom with signal-to-noise ratios of 10-50. We have determined spectral indices over a common range of wavelengths in the rest frames of the quasars between Ly-alpha and C IV emission. Several internal and external checks indicate that the typical errors in the spectral indices are +/- 0.1. We find that quasars with damped Ly-alpha systems in the foreground are stochastically redder than those without damped Ly-alpha systems in the foreground. This difference, significant at the 3 sigma-level, confirms our previous detection in the sample of Sargent, Steidel, & Boksenberg. Combining the Wolfe et al. and Sargent et al. samples increases the significance of the reddening to at least 4 sigma. We compute dust-to-gas ratios from the spectral indices on the assumption that the extinction curve in the damped Ly-alpha systems has the same shape as that in the Milky Way or the Large or Small Magellanic Cloud. Galactic-type dust appears to be ruled out by the absence of strong extinction near 2175 angstrom in the rest frames of several damped Ly-alpha systems. Our best estimates of the typical dust-to-gas ratio in the damped Ly-alpha systems are then 5%-20% of that in the Milky Way. This result, together with recent measurements of the gas-phase abundances of Zn and Cr in three damped Ly-alpha systems, indicates that the overall abundances of heavy elements (in both the gas and solid phases) are about one order of magnitude lower than the Galactic value.