We present and compare results from Monte Carlo and self-consistent-held studies of a grafted brush of polyelectrolyte chains (of length N), interacting via a screened-Coulombic potential. We examine the brush under a variety of grafting and screening conditions and investigate the various regimes of this system. The agreement between Monte Carlo and self-consistent-held methods is quite good. When the effective interaction strength is reasonably large, and the screening is strong, the polyelectrolyte brush behaves like a neutral brush with an effective excluded volume parameter, in agreement with previous scaling studies. For weaker screenings, we find and describe some region where the behavior of the brush height H resembles the H similar to N-3 prediction made by Pincus, and more recently by von Goeler and Muthukumar.