  We study $e^{\pm}$ pair plasmas in pair equilibrium, which emit high energy
radiation by thermal Comptonization of soft photons. We find that the maximum
luminosity to size ratio of the source (i.e. the compactness) depends not only
on the hot plasma temperature, but also on the spectral index of the resulting
Comptonized spectrum. In the observationally interesting range, sources of same
compactness can be hotter if their spectrum is steeper. Instruments observing
in the 50--500 keV energy range, such as OSSE on board CGRO, and especially the
future SAX satellite, can be more successful in detecting sources moderately
steep, the flattest sources being characterized by an high energy cut--off at
too low frequencies. For any given pair of values of spectral index and
temperature, Comptonization theory alone fixes the $ratio$ of the compactnesses
in hard and soft photons. However, if the source is pair dominated, the
absolute values of the two compactnesses are fixed. Therefore there is a a
one--to--one correspondence between the physical parameters of the source (the
compactnesses in soft and hard photons) and the observable quantities (spectral
index and temperature). This correspondence can be extremely useful in
interpreting the physical behaviour of the sources, especially during
variations, and can help discriminating between different models for the high
energy emission of compact sources.
