The evaluation of low-density isochoric measurements on methanol vapor-steam mixtures performed in a large temperature range by our group some years ago proved to be unsatisfactory, because the nonideality behavior as well as the effects of experimental errors, of impurities, of physical and chemical adsorption at the walls of the measuring vessel and of thermal decomposition of the substances at higher temperatures could not separately be treated. Furthermore, the same effects would have already to be taken into account in the evaluation of the measurements on the corresponding pure components to derive reliable second cross virial coefficients B-12. A new analysis of the older measurements on steam considering these influences led to improved values for the second virial coefficient B of steam after all. The evaluation scheme, which is based on isothermal values recalculated using a second-order Taylor series, in terms of temperature, is used to extract more reliable values for B of methanol vapor (373-628 K). In contrast to the findings for steam the measurements on methanol vapor were not influenced by adsorption, but suffered from an unknown impurity. Finally, improved B-12 values of the methanol vapor-steam mixture (373-527 K) were deduced considering the adsorption of the steam as well as the impurity of methanol vapor.