Solid-state NMR is a valuable technique for the study of disordered materials. Analysis of such spectra usually involves solution of so-called ill-posed inverse problems. Here we present a strategy for the analysis of two-parameter two-dimensional NMR problems and test it on 2D DECODER and DOQSY experiments. Using Monte Carlo tests, constraints are determined for the resolution and accuracy of the analysis for both experiments. The methods are finally applied to spectra of spider dragline silk, a heterogeneous solid fibrous protein.