Summary: The effects of additive white noise upon the dynamics of a system described by its Hopf normal form are investigated, with particular reference to the well-known model of a detuned single-mode laser. The power spectrum corresponding to the laser amplitude is determined by finite difference solution of a partial differential equation, and analytical formulas are determined in the asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter in generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where accurate first-eigenvalue approximations of Fokker-Planck equation exist are indicated.