Bulk motion corrupts diffusion measurements in the heart but can be mitigated by nulling first and second gradient moments. When using optimization methods to design diffusion gradient waveforms with moment nulling, imperfect gradient waveforms arise from discrete convergence criteria, which impart residual (non-zero) gradient moments. This leads to intravoxel dephasing, signal loss, and inaccurate ADC measurements. Herein, simulations show that residual M0≤10-2mT/m•s, M1≤10-4mT/m•s2, and M2≤10-5mT/m•s3 leads to ≤5% increase in ADC. This work defines convergence criteria requirements for residual gradient moments that enable faster optimizations and more accurate measurements of ADC when using optimization methods for cardiac DWI sequence design.