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_ν ~ ν^-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 nonthermal particle content of the emitting plasma, as well as the observer orientation relative to the jet axis.