Abstract Realistic fault-tolerant quantum computing at reasonable overhead requires two-qubit gates with&#xD;the highest possible fidelity. Typically, an infidelity of ≲ 10^{-4} is recommended in the literature.&#xD;Focusing on the phase-sensitive architecture used in laboratories and by commercial companies to&#xD;implement quantum computers, we show that even under noise-free, ideal conditions, neglecting&#xD;the carrier term and linearizing the Lamb-Dicke term in the Hamiltonian used for control-pulse&#xD;construction for generating Mølmer-Sørensen XX gates based on the Raman scheme are not justified&#xD;if the goal is an infidelity target of <10^{-4}. We obtain these results with a gate simulator code that,&#xD;in addition to the computational space, explicitly takes the most relevant part of the phonon space&#xD;into account. With the help of a Magnus expansion carried to the third order, keeping terms up to&#xD;the fourth order in the Lamb-Dicke parameters, we identify the leading sources of coherent errors,&#xD;which we show can be eliminated by adding a single linear equation to the phase-space closure&#xD;conditions and subsequently adjusting the amplitude of the control pulse (calibration). This way,&#xD;we obtain XX gates with infidelities < 10^{-4}.