  We demonstrate the feasibility of a strong feedback regime for a
single-electron tunneling device weakly coupled to an underdamped single-mode
oscillator. In this regime, mechanical oscillations are generated and the
current is strongly modified whereas the current noise is parametrically big
with respect to the Poisson value. This regime requires energy dependence of
the tunnel amplitudes. For sufficiently fast tunnel rates the mechanical
contribution to current noise can exceed the Poisson value even beyond the
strong feedback regime.
