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 multi-plane hyperbolic constraint and show that it reduces the overall complexity of the FRP model with minimal penalties in accuracy. For a $120$~km standard single-mode fiber transmission, at $60$~Gbaud with DP-$16$QAM, a complexity reduction of $93$\% is achieved with a performance penalty below $0.1$~dB.