Volume haptics has shown itself an effective way of enhancing precision and speed in interaction with medical or scientific visualization. This paper presents a mixed solver approach for the primitive-based volume haptics problem, to provide the best performance for every volume haptics application. For situations where the constraints are orthogonal we present a fast and high precision analytical solver. For complex configurations requiring support for non-orthogonal constraints we allow for fall-back on a numerical solver. The results show significantly improved performance with the analytical solver, allowing for higher stiffness and thus feedback of higher quality, while still allowing for transparent support for non-orthogonal constraints.