We study models of compact jets in the hard state of black-hole binaries, in which we self-consistently solve for both the steady state electron distribution and the emitted spectrum in both the self-absorbed and optically thin parts as functions of the height along the jet. We take into account synchrotron emission and absorption, Compton scattering of synchrotron, stellar and accretion-flow photons, adiabatic losses, and absorption of very-high energy gamma-rays by pair production on stellar photons. We find Compton upscattering of blackbody stellar radiation in high-mass X-ray binaries to be a major contributor to their gamma-ray emission. Then measurements and/or upper limits on that emission impose strong constraints on the jet parameters, in particular on their magnetic field. We apply our models to the hard state of Cyg X-1, and find it accounts well for its radio/IR spectrum as well its gamma-ray emission observed by Fermi. The Fermi emission and upper limits also place strong constraints on both leptonic and hadronic accretion models.