Off-resonant error for a driven quantum system refers to interactions due to the input drives having non-zero spectral overlap with unwanted system transitions. Here, we quantify off-resonant error for the cross-resonance interaction with application to a direct CNOT gate implementation [1, 2]. We show that pulse parameters should be optimized so that off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Additionally, we show that a Y-DRAG [3, 4] pulse on the control qubit can significantly help to mitigate the effects of off-resonant error. Depending on system parameters, the proposed methods can improve the average off-resonant error by up to an order of magnitude for a direct CNOT calibration.  Petar Jurcevic, Ali Javadi-Abhari, Lev S Bishop, Isaac Lauer, Daniela F Bogorin, Markus Brink, Lauren Capelluto, Oktay Gunluk, Toshinari Itoko, Naoki Kanazawa, et al. “Demonstration of quantum volume 64 on a superconducting quantum computing system”, Quantum Science and Technology, 6(2):025020, 2021.  Abhinav Kandala, Ken X. Wei, Srikanth Srinivasan, Easwar Magesan, Santino Carnevale, George A. Keefe, David Klaus, Oliver Dial, and David C. McKay, “Demonstration of a high-fidelity cnot for fixed-frequency transmons with engineered ZZ suppression”, arXiv preprint quant-ph/2011.07050, 2020.  F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulses for elimination of leakage in weakly nonlinear qubits”. Phys. Rev. Lett., 103:110501, 2009.  Jay M Gambetta, F Motzoi, ST Merkel, and Frank K Wilhelm. “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator”. Physical Review A, 83(1):012308, 2011. *This work was supported by the Intelligence Advanced Research Projects Activity (IARPA) under contract W911NF-16-1-0114.