  Rapid inverse Compton cooling sets in when the brightness temperature (T_B)
of a self-absorbed synchrotron source with power-law electrons reaches ~10^{12}
K. However, T_B inferred from observations of intra-day variable sources (IDV)
are well above the "Compton catastrophe" limit. This can be understood if the
underlying electron distribution cuts off at low energy. We approximate a
low-energy cut-off with monoenergetic electrons. We compute the synchrotron
self-Compton (SSC) spectrum of such distribution, and using the IDV source
S5~0716+714 as an example, we compare it to the observed SED of S5~0716+714.
The hard radio spectrum is well-fitted by this model, and the optical data can
be accommodated by a power-law extension to the electron spectrum. We therefore
examine the scenario of an injection of electrons that is a double power law in
energy with a hard low-energy component that does not contribute to the
synchrotron opacity. We show that the double power-law injection model is in
good agreement with the observed SED of S5~0716+714. For intrinsic variability,
we find that a Doppler factor of D\geq30 can explain the observed SED provided
that low-frequency (<32 GHz) emission originates from a larger region than the
higher-frequency emission. To fit the entire spectrum, D\geq65 is needed. We
find the constraint imposed by induced Compton scattering at high T_B is
insignificant in our model. We confirm that electron distribution with a
low-energy cut-off can explain the high T_B in compact radio sources. We show
that synchrotron spectrum from such distributions naturally accounts for the
observed hard radio continuum with a softer optical component, without the need
for an inhomogeneous source.
