  The coarsening instability typically disrupts steady-state cluster-size
distributions. We show that degradation coupled to the cluster size, such as
arising from biological proteolysis, leads to a novel fixed-point cluster size.
Stochastic evaporative and condensative fluxes determine the width of the
fixed-point size distribution. At the fixed-point, we show how the peak size
and width depend on number, interactions, and proteolytic rate. This
proteolytic size-control mechanism is consistent with the phenomenology of
pseudo-pilus length control in the general secretion pathway of bacteria.
