The bulk acceleration of electron-positron jets in the presence of background radiation is examined, taking account of the conversion of electromagnetic energy into pairs and X-rays through the interaction of the cold e^+/-^ beam with the ambient radiation. It is shown that in order to avoid catastrophic radiative drag, the fraction of total jet power carried by pairs must not exceed the ratio of radiative cooling time of the outflowing pairs by soft photons to dynamical time. This requirement is automatically satisfied, owing to rapid pair annihilation, if the total jet power is not much smaller than the fraction of UV/soft X-ray luminosity intercepted by the inner jet, as measured in the comoving frame. It is found that the flow undergoes a sharp transition whereby the Poynting flux is converted into pairs and beamed X-rays, when the bulk Lorentz factor exceeds the corresponding threshold energy above which the pair-production opacity becomes larger than unity. When the scattered spectrum is sufficiently flat, such that the cooling rate is dominated by hard photons from near its upper cutoff, the Poynting flux is converted mostly into beamed pairs. However, if the scattered spectrum is steep at low energies, like those observed in radio-quiet sources, there is catastrophic X-ray production. The implications for jets from blazars are considered, and several ways in which X-ray overproduction may he avoided are discussed.