European Union adopted the Regulation (EU) No 537/2014, which in practice prohibits the joint provision of audit and most types of non-audit services (NAS). Regulators presume that NAS fees weaken auditor independence and, as a result, impair audit quality. As the evidence at the European level does not support this view, the question of whether the new regulation will enhance auditor independence remains open. We examine the association between future NAS fees and audit quality by distinguishing among tax, audit-related and other services. We base the analysis on a sample of Spanish listed companies for the period between 2005 and 2016, finding a consistent negative association between future other NAS fees and audit quality. This suggests that the expectation of future purchases of this type of NAS may impair auditor independence. Conversely, for tax and audit-related services results are not significant. Taken together, results suggest that European regulators should seek for further evidence before banning NAS, as some of them may in fact enhance audit quality.