  We investigate the distribution of instanton sizes in the framework of a
simplified model for ensembles of instantons. This model takes into account the
non-diluteness of instantons. The infrared problem for the integration over
instanton sizes is dealt with in a self-consistent manner by approximating
instanton interactions by a repulsive hard core potential. This leads to a
dynamical suppression of large instantons. The characteristic features of the
instanton size distribution are studied by means of analytic and Monte Carlo
methods. In one dimension exact results can be derived. In any dimension we
find a power law behaviour for small sizes, consistent with the semi-classical
results. At large instanton sizes the distribution decays exponentially. The
results are compared with those from lattice simulations.
