  The suspension noise in interferometric gravitational wave detectors is
caused by losses at the top and the bottom attachments of each suspension
fiber. We use the Fluctuation-Dissipation theorem to argue that by careful
positioning of the laser beam spot on the mirror face it is possible to reduce
the contribution of the bottom attachment point to the suspension noise by
several orders of magnitude. For example, for the initial and enhanced LIGO
design parameters (i.e. mirror masses and sizes, and suspension fibers' lengths
and diameters) we predict a reduction of $\sim 100$ in the "bottom" spectral
density throughout the band $35-100\hbox{Hz}$ of serious thermal noise. We then
propose a readout scheme which suppresses the suspension noise contribution of
the top attachment point. The idea is to monitor an averaged horizontal
displacement of the fiber of length $ l$; this allows one to record the
contribution of the top attachment point to the suspension noise, and later
subtract it it from the interferometer readout. For enhanced LIGO this would
allow a suppression factor about 100 in spectral density of suspension thermal
noise.
