We study the average frequency shift W of the phase of the electric fi
eld in a laser described by the extended Lorenz model. We discuss new
properties of W for parameter ranges where the motion is periodic or c
haotic. These properties are invariant with respect to the laser frequ
ency of the reference frame and are robust with respect to the main bi
furcation parameters given by the incoherent pump and the atom-cavity
detuning.