  We uncover a highly non-trivial dependence of the spin-noise (SN) resonance
broadening induced by the intense probe beam. The measurements were performed
by probing the cell with cesium vapor at the wavelengths of the transition
${6}^2S_{1/2} \leftrightarrow {6}^2P_{3/2}$ ($\mathrm{D}_2$ line) with
unresolved hyperfine structure of the excited state. The light-induced
broadening of the SN resonance was found to be strongly different at different
slopes of the $\mathrm{D}_2$ line and, generally, varied nonmonotonically with
the light power. We discuss the effect in terms of the phenomenological Bloch
equations for the spin fluctuations and demonstrate that the SN broadening
behavior strongly depends on the relation between the pumping and excited level
decay rates, the spin precession and decoherence rates. To reconcile the
puzzling experimental results, we propose that the degree of optical
perturbation of the spin-system is controlled by the route of the excited-state
relaxation of the atom or, in other words, that the act of optical excitation
of the atom does not necessarily breaks down completely its ground-state
coherence and continuity of the spin precession. Spectral asymmetry of the
effect, in this case, is provided by position of the `closed' transition $F = 4
\leftrightarrow F = 5$ at the short-wavelength side of the line. This
hypothesis, however, remains to be proven by microscopic calculations.
