  We find that energy losses due to synchrotron self-Compton (SSC) emission in
blazar jets can produce distinctive signatures in the time-averaged synchrotron
and SSC spectra of these objects. For a fairly broad range of particle
injection distributions, SSC-loss dominated synchrotron emission exhibits a
spectral dependence $F_\nu \sim \nu^{-3/2}$. The presence or absence of this
dependence in the optical and ultraviolet spectra of flat spectrum radio
quasars such as 3C~279 and in the soft X-ray spectra of high frequency BL Lac
objects such as Mrk 501 gives a robust measure of the importance of SSC losses.
Furthermore, for partially cooled particle distributions, spectral breaks of
varying sizes can appear in the synchrotron and SSC spectra and will be related
to the spectral indices of the emission below the break. These spectral
signatures place constraints on the size scale and the non-thermal particle
content of the emitting plasma as well as the observer orientation relative to
the jet axis.
