Large low-frequency noise is found in some perovskite relaxor ferreoelectrics when they are polarized, regardless of whether the polarization is accompanied by an applied electric field. The noise appears both in the ferroelectric and relaxor states, including in the nominally ergodic paraelectric state at temperatures above the susceptibility peak. Since it is present whenever the samples are microphonic due to piezoelectricity but not evident when they are not microphonic, it appears to be a response to mechanical strain changes. Dependence of the noise on sample thermal history indicates that non-equilibrium strain relaxation is the source, even in the temperature range for which the sample is nominally ergodic. Non-equilibrium noise in the absence of net piezoelectricity is found at somewhat higher frequencies.