The kinetic molecular mechanism (KMM) for the onset of avalanche condensation from supersaturated vapors, described in this report, is more general than the one we used previously. While the expressions for the rate constants needed to compute the steady-state populations are the same, additional steps were introduced to take into account cluster growth via accretions with dimers. In the present version, the magnitudes for the stepwise enthalpy decrements are assigned using all the "best'' available experimental and computed values, so that the program requires less arbitrary adjustable parameters. The derived values for the entropy decrements upon successive accretions present a basis for estimating the total entropy of clusters (size n), and thus impose constraints on any model for dynamics within clusters. For high ambient pressures an option is provided for correcting the condensation rate constants due to restricted diffusion of accreting units (monomers or dimers) into the reaction shell of the growing clusters. Published data for condensation flux levels in supersaturated methanol are reanalyzed to illustrate the use of the newly developed code.