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We use  N ‐body simulations to investigate the radial dependence of the density, ρ, and velocity dispersion, σ, in cold dark matter (CDM) haloes. In particular, we explore how closely   Q ≡ρ/σ 3  , a surrogate measure of the phase‐space density, follows a power law in radius. Our study extends earlier work by considering, in addition to spherically averaged profiles, local  Q  estimates for individual particles,   Q i   ; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo,   Q i  ( r ′) ; and by carefully removing substructures in order to focus on the profile of the smooth halo,   Q  s  . The resulting   Q  s   i  ( r ′)  profiles follow closely a power law near the centre, but show a clear upturn from this trend near the virial radius,  r  200 . The location and magnitude of the deviations are in excellent agreement with the predictions from Bertschinger's spherical secondary‐infall similarity solution. In this model,   Q ∝ r  −1.875   in the inner, virialized regions, but departures from a power‐law occur near  r  200  because of the proximity of this radius to the location of the first shell crossing – the shock radius in the case of a collisional fluid. Particles there have not yet fully virialized, and so  Q  departs from the inner power‐law profile. Our results imply that the power‐law nature of  Q  profiles only applies to the inner regions and cannot be used to predict accurately the structure of CDM haloes beyond their characteristic scale radius.

Secondary infall and the pseudo‐phase‐space density profiles of cold dark matter haloes