  For future configurations, we study the relation between the abatement of the
noise sources and the Signal to Noise Ratio (SNR) for coalescing binaries. Our
aim is not the proposition of a new design, but an indication of where in the
bandwidth or for which noise source, a noise reduction would be most efficient.
We take VIRGO as the reference for our considerations, solely applicable to the
inspiralling phase of a coalescing binary. Thus, only neutron stars and small
black holes of few solar masses are encompassed by our analysis. The
contributions to the SNR given by final merge and quasi-normal ringing are
neglected. It is identified that i) the reduction in the mirror thermal noise
band provides the highest gain for the SNR, when the VIRGO bandwidth is divided
according to the dominant noises; ii) it exists a specific frequency at which
lies the potential largest increment in the SNR, and that the enlargement of
the bandwidth, where the noise is reduced, produces a shift of such optimal
frequency to higher values; iii) the abatement of the pendulum thermal noise
provides the largest, but modest, gain, when noise sources are considered
separately. Our recent astrophysical analysis on event rates for neutron stars
leads to a detection rate of one every 148 or 125 years for VIRGO and LIGO,
respectively, while a recently proposed and improved, but still conservative,
VIRGO configuration would provide an increase to 1.5 events per year. Instead,
a bi-monthly event rate, similar to advanced LIGO, requires a 16 times gain. We
analyse the 3D (pendulum, mirror, shot noises) parameter space showing how such
gain could be achieved.
