Resonance assignment of NMR spectra of unstructured proteins is made difficult by severe overlap due to the lack of secondary structure. Fortunately, this drawback is partially counterbalanced by the narrow line-widths due to the internal flexibility. Alternate sampling schemes can be used to achieve better resolution in less experimental time. Deterministic schemes (such as radial sampling) suffer however from the presence of systematic artifacts. Random acquisition patterns can alleviate this problem by randomizing the artifacts. We show in this communication that quantitative well-resolved spectra can be obtained, provided that the data points are properly weighted before FT. These weights can be evaluated using the concept of Voronoi cells associated with the data points. The introduced artifacts do not affect the direct surrounding of the peaks and thus do not alter the amplitude and frequency of the signals. This procedure is illustrated on 60-residue viral protein, which lacks any persistent secondary structure and thus exhibits major signal overlap.