We report on a study of spherical polyelectrolyte brushes that consist of a solid core onto which linear polyelectrolyte chains are chemically grafted. The core particles are made up of solid poly(styrene) and have a radius R of ca. 50 nm. As polyelectrolyte chains the weak polyelectrolyte poly(acrylic acid) or the strong polyelectrolyte poly(styrenesulfonate) was used. These chains were generated directly on the surface of the core particles by a grafting-from technique. Hence, the chains are chemically bound to the surface but can be cleaved off and analyzed separately. The contour length $L_c$ and the number of grafted chains per unit area $\sigma$ can thus be determined accurately. The thickness L of the brush layer on the surface has been determined by dynamic light scattering. It is measured for different $L_c/R$ as a function of $p\mathrm{H},$ ionic strength, and valency of counterions. Annealed brushes exhibit a transition with increasing $p\mathrm{H}$ in which the chains are stretched to nearly full length. This can be traced back to the building up of the osmotic pressure of the counterions. The brush height L decreases considerably with increasing ionic strength, most notably when adding divalent ions. The entire set of L as a function of R, $L_c,$ and $\sigma$ can be fully explained in terms of a simple two-parameter theory developed by Hariharan et al. [Macromolecules 31, 7514 (1998)].