The magnetic field generation in a simple solenoid is reconsidered for the case where the magnetic field is generated by a superconductor with anisotropy in its critical current density. In this case the influence of the radial magnetic field at the solenoid ends on the weak direction of the conductor has to be taken into account. Instead of the usual load line which stems from the maximum axial field at the inner turns, two load lines must be considered: one as usual, and the second one representing the radial field at the coil end. The maximum field generated by the solenoid is determined by which load line meets its respective jc-H curve first. For tapes of (Bi,Pb)2Sr2Ca2Cu3Ox it is the radial field at the solenoid ends which determines the central field which can be generated by the solenoid. This is also the case for most other anisotropic superconductors even with a moderate jc anisotropy of, for example, two. Insert coils in a background field can significantly raise the maximum central field as the ratio between axial and radial fields is different. This gain for a magnet made from Bi(2223) tapes is of the order of 30% (at T= 77 K). Some alternatives for maximum field generation using anisotropic tapes are discussed.