  We report the confinement of an optomechanical micro-oscillator in a squeezed
thermal state, obtained by parametric modulation of the optical spring. We
propose and implement an experimental scheme based on parametric feedback
control of the oscillator, which stabilizes the amplified quadrature while
leaving the orthogonal one unaffected. This technique allows us to surpass the
-3dB limit in the noise reduction, associated to parametric resonance, with a
best experimental result of -7.4dB. In a moderately cooled system, our
technique can be efficiently exploited to produce strong squeezing of a
macroscopic mechanical oscillator below the zero-point motion.
