  We report on a laser based $^{199}$Hg co-magnetometer deployed in an
experiment searching for a permanent electric dipole moment of the neutron. We
demonstrate a more than five times increased signal to-noise-ratio in a direct
comparison measurement with its $^{204}$Hg discharge bulb-based predecessor. An
improved data model for the extraction of important system parameters such as
the degrees of absorption and polarization is derived. Laser- and lamp-based
data-sets can be consistently described by the improved model which permits to
compare measurements using the two different light sources and to explain the
increase in magnetometer performance. The laser-based magnetometer satisfies
the magnetic field sensitivity requirements for the next generation nEDM
experiments.
