Compact anisotropic spheres with prescribed energy density

New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav. 21, 899 905 (1989)), and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav. 26, 75 84 (1994)), as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.