Abstract. Rotational discontinuities (RDs) are governed by two relations: the Walén relation predicting that the plasma velocity observed in the deHoffmann–Teller frame equals the local Alfvén velocity and another relation that connects the variation in plasma mass density, ρ, to variations in the pressure anisotropy factor, α, defined as α: ≡(p_∥ − p_⊥) μ₀/B², so that ρ(1 − α) is constant. While the Walén relation has become a standard tool for classifying magnetopause crossings as RDs , the ρ(1 − α)= const. condition has never been directly verified at the same time, largely due to problems with determining ρ when no ion composition measurements were available. In fact, to overcome the lack of composition information, the validity of the relation has often been assumed and the Walén relation reformulated so that variations in ρ are replaced by variations in α. In this paper we exploit the availability of high-time-resolution composition measurements on the Cluster spacecraft to directly test the ρ (1− α)= const. condition for three magnetopause crossings, identified as RDs from the application of the Walén relation to measurements of plasma ions and magnetic field by the CIS (Cluster Ion Spectrometry) and FGM (flux-gate magnetometer) instruments, respectively. We find that the relation is not fulfilled in either case. In one event, with a fairly large content of oxygen ions, the Walén test improved when the contribution from these ions was taken into account. Through comparisons of the measured ion densities with simultaneously measured total electron densities by the Waves of HIgh frequency and Sounder for Probing of Electron density by Relaxation (WHISPER) instrument, we were able to exclude the possibility that ion populations hidden to the CIS instrument because of their very low energies could have changed ρ to match the ρ(1 − α)= const. condition. We also excluded the possibility that energetic ions above the CIS energy range could have sufficiently changed the true α. It thus appears that the ρ(1 − α)= const. condition, for reasons not presently understood, is not valid for the kind of RD-like structures we observe.