To establish noise levels for the borehole strainmeters of the Plate Boundary Observatory (PBO), we have analyzed data recorded by eight of these instruments, all in the Anza region of southern California. We determine time-varying power spectra for frequencies from 10-3 to 10 Hz, using a new method that combines multitaper spectrum estimation, smoothing by local regression, and computation of cumulative distribution functions. From about 2 Hz to the Nyquist frequency of 10 Hz, the noise floor is set by instrument resolution; for frequencies between 0.1 Hz and 1 Hz, it is set by microseisms. The lowest noise level is between 0.01 and 0.1 Hz, with a rapid increase at lower frequencies. However, in most instruments this low-noise range also contains narrowband noise that appears to be caused by power supply fluctuations. We compare these results with noise spectra from other types of strainmeters, which suggest two conclusions: (1) they are in agreement with results for surficial, long-baseline instruments; and (2) other subsurface strainmeters have lower noise in the seismic band than the PBO instruments do.