We analyze the possibility of using a low-background Ge-NaI spectromet
er in a reactor experiment aimed at searches for the neutrino magnetic
moment down to 3 x 10(-11) of the electron magneton. The propel ties
of the so-far existing low-background Ge spectrometers are discussed,
and additional sources of background in a reactor experiment at a smal
l 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 mwe with a dedicated spectrometer b
uilt at ITEP are reported.