  We address a phase estimation scheme using Gaussian states in the presence of
non-Gaussian phase noise. At variance with previous analysis, we analyze
situations in which the noise occurs before encoding phase information. In
particular, we study how squeezing may be profitably used before or after phase
diffusion. Our results show that squeezing the probe after the noise greatly
enhances the sensitivity of the estimation scheme, as witnessed by the increase
of the quantum Fisher information. We then consider a realistic setup where
homodyne detection is employed at the measurement stage, and address its
optimality as well as its performance in the two different scenarios.
