SABRE (Signal Amplification by Reversible Exchange) methods provide a simple, fast, and cost-effective method to hyperpolarize a wide variety of molecules in solution, and have been demonstrated with protons and, more recently, with heteronuclei (X-SABRE). The conventional analysis of the SABRE effect is based on level anti-crossings (LACs), which requires very low magnetic fields (~ 0.6μT) to achieve resonance and transfer spin order from the para-hydrogen to target heteronuclei. We have demonstrated in our recent study that the validity of LACs used in SABRE is very limited, so the maximum SABRE polarization predicted with LACs is not correct. Here, we present several oscillating pulse sequences that use magnetic fields far away from the resonance condition and can commonly triple the polarization. An analysis with average Hamiltonian theory indicates that the oscillating pulse, in effect, adjusts the J-couplings between hydrides and target nuclei and that a much weaker coupling produces maximum polarization. This theoretical treatment, combined with simulations and experiment, show substantial magnetization improvements relative to traditional X-SABRE methods. It also shows that, in contrast to most pulse sequence applications, waveforms with reduced time symmetry in the toggling frame make magnetization generation more robust to experimental imperfections