We outline an important advance in the problem of obtaining a two-dimensional (2D) line list of the most prominent features in a 2D high-resolution NMR spectrum in the presence of noise, when using the Filter Diagonalization Method (FDM) to sidestep limitations of conventional FFT processing. Although respectable absorption-mode spectra have been obtained previously by the artifice of "averaging" several FDM calculations, no 2D line list could be directly obtained from the averaged spectrum, and each calculation produced numerical artifacts that were demonstrably inconsistent with the measured data, but which could not be removed a posteriori. By regularizing the intrinsically ill-defined generalized eigenvalue problem that FDM poses, in a particular quite plausible way, features that are weak or stem from numerical problems are attenuated, allowing better characterization of the dominant spectral features. We call the new algorithm FDM2K.