Diffusion-Weighted MRI (DW-MRI) often suffers from signal attenuation due to long TE, motion-related artefacts, dephasing due to concomitant gradients (CGs), and image distortions due to eddy currents (ECs). Further, the application of rapidly switching gradients may cause peripheral nerve stimulation (PNS). These challenges hinder the progress, application and interpretability of DW-MRI. Therefore, based on the Optimized Diffusion-weighting Gradient waveforms Design (ODGD) formulation, in this work we design optimal (minimum TE) nth-order moment-nulling diffusion-weighting gradient waveforms with or without CG-nulling able to reduce EC induced distortions and PNS-effects. We assessed the feasibility of these waveforms in simulations and phantom experiments.