  A new Compton longitudinal polarimeter currently under construction for HERA
is presented. The key component of the polarimeter is a Fabry-Perot cavity
located around the electron beam pipe. With such an optical cavity, a
continuous laser power equivalent to 5 kW, much higher than those commercially
available, can be achieved, leading to one backscattered photon per bunch
crossing. This ``few-photon mode'' will allow a very precise determination of
the calorimeter response with little systematic uncertainty. The electron
polarization measurement at the per mill level is expected.
