Euro-Atlantic regimes are typically identified using either the latitude of the eddy-driven jet, or clustering algorithms in the phase space of 500hPa geopotential height (Z500). However, while robust trimodality is visibly apparent in jet latitude indices, Z500 clusters require highly sensitive significance tests to distinguish them from autocorrelated noise... As a result, even small shifts in the time-period considered can notably alter the diagnosed regimes. Fixing the optimal regime number is also hard to justify. We argue that the jet speed, a near-Gaussian distribution projecting strongly onto the Z500 field, is the source of this lack of robustness. Once its influence is removed, the Z500 phase space becomes visibly non-Gaussian, and clustering algorithms easily recover three extremely stable regimes, corresponding to the jet latitude regimes. Further analysis supports the existence of two additional regimes, corresponding to a tilted and split jet. This framework therefore naturally unifies the two regime perspectives. (read more)