  It is well known that, in the Boltzmann-Grad limit, the distribution of the
free path length in the Lorentz gas with disordered scatterer configuration has
an exponential density. If, on the other hand, the scatterers are located at
the vertices of a Euclidean lattice, the density has a power-law tail
proportional to xi^{-3}. In the present paper we construct scatterer
configurations whose free path lengths have a distribution with tail xi^{-N-2}
for any positive integer N. We also discuss the properties of the random flight
process that describes the Lorentz gas in the Boltzmann-Grad limit. The
convergence of the distribution of the free path length follows from
equidistribution of large spheres in products of certain homogeneous spaces,
which in turn is a consequence of Ratner's measure classification theorem.
