The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled C-13 solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations (e.g. two-bond C-13-C-13 correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra. (C) 2007 Elsevier Inc. All rights reserved.