Using a refocused INADEQUATE NMR experiment we show that homonuclear carbon-carbon through-bond correlations can be obtained in disordered organic solids where the line widths greatly exceed the value of the scalar coupling. The feasibility of the experiment is demonstrated for inhomogeneous samples of C-13-labeled wood and cellulose. The two-dimensional correlation maps are used to assign unambiguously the carbon resonances of this natural polymer. We show that the efficiency of the refocused INADEQUATE experiment depends on the ratio T'(2)/T-2(), where T-2() is the apparent relaxation time, deduced from the line width, and T-2(') is the transverse dephasing time measured in a spin-echo experiment. For cellulose, we find that T'(2) is larger than T-2() by more than 1 order of magnitude and that the experimental efficiency of the refocused INADEQUATE experiment is around 10%, in agreement with calculations. Even in ordinary crystalline organic solids, such as powdered amino acids, large differences are observed between T'(2) and T-2().