We have developed a new method for determining the radial volume dust density profiles of dark clouds. We have applied this method to co-added IRAS data of 12 small molecular clouds (Bok globules). Raw 60 and 100-mu-m images were used to generate median filtered backgrounds to be subtracted from the original images. From the resulting differenced images, dust temperature and dust optical depth maps were generated using a single-temperature blackbody model and a dust emissivity proportional to lambda-1. These clouds were resolved at the longest IRAS wavelengths and exhibit both regular shapes and structural simplicity. To extract radial dust volume density power laws of the form n(r) is-proportional-to r-gamma, a collection of dust optical depth contour levels was fitted with ellipses, and the slope of the run of log (column density) versus log (impact parameter) was determined. Modeling enabled determining a relation between the column density power law and the volume density power law for finite-sized clouds. The volume indices gamma were found to be in the range 1 to 5/2, in agreement with previous studies of the gas density. Our rather soft dust indices do not support the hypothesis of grain settlement into the cores of these clouds. However, given the spread in observed indices, the magnitude of a necessary correction for clouds of finite size, and the uncertainties in using a single-temperature blackbody model for IRAS data, determination of the dynamical state of these clouds from IRAS data via this method is not currently reliable.