Experimental absorption spectral data from e-branch line mixing in HCN, C2H2, and N2O are inverted to extract their respective relaxation W matrices. The formulation makes use of a general iterative inversion algorithm based upon first-order sensitivity analysis and Tikhonov regularization. The algorithm, previously applied to R-branch Line mixing in HCN, is reformulated to explicitly require detailed balance for the real, off-diagonal W matrix elements. As with the HCN R-branch case, the W matrices recovered typically were found to describe line mixing much better than those derived from the fitting laws currently in use, and the inversion algorithm usually converged within just three iterations.