The comply-or-explain principle is a central element in the EU corporate governance framework which was put in place by Directive 2006/46/EC. Whilst avoiding an inflexible “one size fits all” approach, the principle has lately been questioned because of the quality of corporate governance reports it has allowed European companies to produce; these companies can either comply with code provisions, or may explain why they do not comply, i.e., why they deviate from a provision of the code. Seidl et al. (2012), in analysing 257 listed companies that had produced some 715 records of deviations, and their respective “explanations”, found that, in contrast to the original idea of comply-or-explain, which emphasised the possibility of justifying deviations with situation-specific reasons, a significant number of the deviations analysed were either not justified at all (that is, they were simply disclosed) or were justified on the basis of objections of principle (e.g., that the code provisions were inappropriate because they failed to embody best practice). An increasing number of studies provide evidence that corporate governance statements disclosed on European stock markets lack quality, mainly in terms of the explanations they include when the companies do not comply with code provisions. In addressing this issue, the European Commission launched a wide-ranging consultation seeking views on how the “explain” approach could be improved. From this consultation we analysed 244 stakeholders’ responses, generating an empirically derived taxonomy of responses. First, we examine these by providing a descriptive account of the different ways in which stakeholders agree that the “explain” option should be used, and what kind of alternative solutions companies should disclose. Second, we discuss the possible implications for code regimes and for management control.