Recovery of the pressure profile is examined for the W7-AS stellaratoron an equilibrium database using only simulated diagnostic informationfrom external magnetic probes. This analysis establishes the extentof profile-relevant information contained in an extensive set ofexternal magnetic data in isolation from measurement error, hitherto asubject of some debate. It is demonstrated that the profile can berecovered up to and including an average profile and a peaking factor.The implications for magnetic-based stellarator equilibriumreconstructions are considered.