We extend prior work on laser pumped helium-4 magnetometers to include the effects of an arbitrary three-dimensional Jones vector for the laser light, general arrangement of the H₁ coils, arbitrary orientation of the elements of the instrument, both ranks of the spin-1 state, the Bloch-Siegert shift, and the virtual light shift. The theoretical equations are solved for several specific cases, as well as the general steady-state case, and theoretical plots are shown in cases of practical interest and for parameters that highlight unexpected or previously-unmodeled effects. A detailed examination of the consequences to the quality of the results is made for several of the approximations used. An improved arrangement of the apparatus is suggested for the case of linearly-polarized light. Comparisons are made between experimental data and theory for several modes of operation. The new model is useful for quickly identifying the appropriate parameters to use in order to optimize the sensitivity of double-resonance helium-4 magnetometers.