  We introduce a method to constrain the characteristic angular size of the
brightest cosmic-ray sources observed above 57 \times 1018 eV. By angular size
of a source, we mean the effective angular extent over which cosmic-rays from
that source arrive at earth. The method is based on the small-scale (< 10\circ)
self-clustering of cosmic-ray arrival directions. The method is applicable to
sparse data sets in which strong localizations of CR* directions are not yet
observed. We show that useful constraints on the source size can be made in the
near future and that these constraints are not strongly dependent on the
assumed spatial distribution and luminosity function of the cosmic-ray sources.
We suggest that an indication of the source size is quite telling. For example,
an indication of the source size can be used to infer limits on the particle
charge and intervening magnetic fields (not independently), both of which are
not well constrained so far. This is possible because the source size is
similar in scale to the magnetic deflection.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics