We propose an approach for constraining the set of nonlinear coefficients of the conventional first-order regular perturbation (FRP) model of the Manakov Equation. We identify the largest contributions in the FRP model and provide geometrical insights into the distribution of their magnitudes in a three-dimensional space. As a result, a multi-plane hyperbolic constraint is introduced. A closed-form upper bound on the constrained set of nonlinear coefficients is given. We also report on the performance characterization of the FRP with multiplane hyperbolic constraint and show that it reduces the overall complexity with minimal penalties in accuracy. For a 120 km standard single-mode fiber transmission, at 60 Gbaud with DP-16QAM, a complexity reduction of 93% is achieved with a performance penalty below 0.1 dB.