  We analyze the possibility of using a low-background Ge-NaI spectrometer in a
reactor experiment for a search for neutrino magnetic moment down to $3 \times
10^{-11}$ of the electron magneton. The properties of the so-far existing Ge
low-background spectrometers are discussed and additional sources of background
in a reactor experiment at a small depth are estimated. These estimates place
specific requirements on the design of the spectrometer. The results of
preliminary background measurements at a small depth of 5 m.w.e. with a
dedicated spectrometer built in ITEP are reported.
