Pure-shift NMR enhances spectral resolution, but the optimal resolution can only be obtained at the cost of acquisition time. We propose to accelerate pure-shift acquisition using optimised ‘burst’ non-uniform sampling schemes [I. E. Ndukwe, A. Shchukina, K. Kazimierczuk and C. P. Butts, Chem. Commun., 2016, 52, 12769] and then reconstruct the undersampled signal mathematically. Here, we focus on the reliability of this reconstruction depending on the sampling scheme and present a workflow for the sampling optimization. It is ready to be implemented in routine measurements and yields a great improvement in reconstruction of challenging cases.