Analysis and interpretation of dispersed vitrinite reflectance data in regions of high thermal maturity (> 2% vitrinite reflectance) have been equivocal partly because of an increase in width and complexity of reflectance histograms with increasing mean reflectance. Such complexity is illustrated by random reflectance (Rran) data from the Arkoma Basin that display a linear increase in standard deviation of Rran with an increase in mean Rran from 1 to 5%. Evaluating how much of the dispersion in these data is the result of vitrinite anisotropy and how much is the result of mixing of kerogen populations by sedimentary processes and/or sampling procedures has been problematic. Automated collection of reflectance data during polarizer rotation provides preliminary data for solution of this problem. Rotational reflectance data collected from a subset of Arkoma Basin samples reveal positive, linear relationships among maximum (R???max), random (Rran), rotational (Rrot), and minimum (R???min) reflectance, as well as a systematic increase in bireflectance (R???max-R???min) with increasing reflectance. R???max and Rrot display lower standard deviations and narrower, more nearly unimodal histograms than Rran and R???min, suggesting that R???max and Rrot are superior (less ambiguous) indices of thermal maturity. These data patterns are inferred to be mostly an indication of increasing vitrinite anisotropy with increasing thermal maturity, suggesting that the linear covariance observed between mean Rran and standard deviation in dispersed organic data sets from regions of high thermal maturity may be explained mostly as the result of increasing vitrinite anisotropy with increasing thermal maturity. ?? 1993.