  We present theoretical results that demonstrate a new technique to be used to
improve the sensitivity of thermal noise measurements: intra-cavity intensity
stabilisation. It is demonstrated that electro-optic feedback can be used to
reduce intra-cavity intensity fluctuations, and the consequent radiation
pressure fluctuations, by a factor of two below the quantum noise limit. We
show that this is achievable in the presence of large classical intensity
fluctuations on the incident laser beam. The benefits of this scheme are a
consequence of the sub-Poissonian intensity statistics of the field inside a
feedback loop, and the quantum non-demolition nature of radiation pressure
noise as a readout system for the intra-cavity intensity fluctuations.
