We here report on the influence of heteronuclear dipolar decoupling on the Al-27 3QMAS, 5QMAS, and the double-quantum filter-satellite-transition magic-angle spinning (DQF-STMAS) spectra of a strongly dipolar-coupled system, gibbsite. The requirements for heteronuclear dipolar decoupling increase with the order of coherence evolving in the indirect dimension of a two-dimensional (2D) experiment. The isotropic line width of the high-resolution 2D spectra, in samples like gibbsite, is composed of four parts: the distribution of isotropic shifts (delta(ISO), delta(QIS)), the homogeneous broadening related to the proton-proton flip-flop terms, the Al-27-Al-27 homonulcear dipolar couplings, and the H-1-Al-27 heteronuclear dipolar couplings. It is shown that, even in the case of gibbsite, where a strong proton-proton bath exists, the main resolution limiting factor in these experiments resides in the H-1-Al-27 dipolar interaction. Copyright (C) 2008 John Wiley & Sons, Ltd.