We generalize the reference model [Optics Comm. 107 (1994) 245] of a multimode laser to include an arbitrary loss ratek . As a result, the decay rates and the oscillation frequencies of the laser relaxation are both k-dependent. Perfect antiphased dynamics is shown to remain, no matter what value is assumed by k. However, depending on k, the oscillatory component of the dynamics may be quenched either partially or completely. For a given k, there exists a cut-off mode number and a set of critical laser parameters separating domains where oscillations occur from domains where there are no oscillations.