We study models of the γ-ray emission of Cyg X-3 observed by Fermi. We calculate the average X-ray spectrum during the γ-ray active periods. Then, we calculate spectra from Compton scattering of a photon beam into a given direction by isotropic relativistic electrons with a power-law distribution, both based on the Klein–Nishina cross-section and in the Thomson limit. Applying the results to scattering of stellar blackbody radiation in the inner jet of Cyg X-3, we find that a low-energy break in the electron distribution at a Lorentz factor of ∼300–103 is required by the shape of the observed X-ray/γ-ray spectrum in order to avoid overproducing the observed X-ray flux. The electrons giving rise to the observed γ-rays are efficiently cooled by Compton scattering, and the power-law index of the acceleration process is ≃2.5–3. The bulk Lorentz factor of the jet and the kinetic power before the dissipation region depend on the fraction of the dissipation power supplied to the electrons; if it is ≃1/2, the Lorentz factor is ∼2.5, and the kinetic power is ∼1038 erg s−1, which represents a firm lower limit on the jet power, and is comparable to the bolometric luminosity of Cyg X-3. Most of the power supplied to the electrons is radiated. The broad-band spectrum constrains the synchrotron and self-Compton emission from the γ-ray emitting electrons, which requires the magnetic field to be relatively weak, with the magnetic energy density ≲ a few times 10−3 of that in the electrons. The actual value of the magnetic field strength can be inferred from a future simultaneous measurement of the infrared and γ-ray fluxes.