Results. We conclude that the inferred Vsin i is smaller than implied by the actual equatorial linear rotation velocity Veq if the stars rotate with alpha < 0, but is larger if the stars have alpha > 0. For a given vertical bar alpha vertical bar the deviations of Vsin i are larger when alpha < 0. If the studied Be stars have on average alpha < 0, the number of rotators with Veq ' 0 : 9Vc is larger than expected from the observed distribution Phi(u); if these stars have on average alpha > 0, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried by Vsin i and, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.