In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either user is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We translate the optimal schemes in the deterministic channel model to the Gaussian channel model, and also derive two upper bounds on the constrained sum-capacity. Numerical evaluations show that the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Gaussian Han-Kobayashi schemes and that with single message schemes.