We introduce a general method of restoring detailed information about the population flow in molecules under non-local-thermodynamic-equilibrium (NLTE) conditions. This information is usually discarded in numerical algorithms which generate only a solution. We apply the method to tracing the pumping schemes for OH in models that represent three common astrophysical maser environments: the envelopes of asymptotic-giant-branch (AGB) stars, the envelopes of red supergiants, and Galactic star-forming regions. In all three of these cases, we show that a large fraction, typically 0.8 or more, of the maser inversion can be recovered from a set of routes that depend on a much smaller fraction (considerably less than 0.1) of the total number of input coefficients to the model. Therefore, these cases display underlying simplicity in the pumping scheme.