Abstract: Analytic approaches to efficiently simulate accurate light transport in homogeneous participating media have recently received attention in the graphics community, and although a closed-form solution to the single-scattering air-light integral has been derived for a generic representation of 1-D angular distributions, its high order of computational complexity alas limits its practical applicability. In this paper, we introduce alternative algebraic formulations of the solution that entirely preserve its closed-form nature while effectively reducing its order of complexity. The analytic derivations yield a significant decrease in the computational cost of the evaluation scheme, and the substantial gains in performance achieved by the method make high-quality light transport simulation considerably more applicable to both real-time and off-line rendering.