The effects of confining a polyelectrolyte solution containing a polyion and its counterions in spherical cavities of different sizes have been investigated by Monte Carlo simulations using a simple model system. Polyions of three different linear charge densities and counterions of three different valences have been examined. Structure, energy, and free energy properties of all systems have been determined as a function of the sphere radius. In nearly all cases, the free energy of confining the polyelectrolyte solution increases as the sphere radius is decreased. The free energy cost decreases as the linear charge density of the polyion is reduced and as the counterion valence is increased, although for completely different reasons. A strong consistency among the variations of the different structural and thermodynamic results on the linear charge density and counterion valence was found. The study provides information relevant for experimental systems of polyions confined to, e.g., viruses, vesicles, and zeolite cavities.