  At the plasmon resonance, high Joule losses in a metal nanoparticle of a
spaser result in its low Q-factor. Due to the latter, to achieve the spasing
regime, in which the number of coherent plasmons exceeds the number of
incoherent plasmons, unsustainably high pump rates may be required. We show
that under the condition of loss compensation by a spaser driven by an external
optical wave, the number of coherent plasmons increases dramatically, and the
quantum noise is suppressed. Since the compensation of losses of the driving
wave may occur even near the spasing threshold, the number of coherent plasmons
may exceed the number of spontaneously excited plasmons at achievable pump
rates.
