The gradient-selected triple-quantum-filtered (GS3Q) esperiment, developed to improve the contrast in NMR imaging of sodium-23 (23Na) in the human brain, is limited by low signal-to-noise ratio (SNR). We have analyzed the GS3Q experiment and show here that the improvement in GS3Q-filtered 32Na SNR as the repetition time (TR) decreases is accompanied by the appearance of spurious one-quantum (1Q) 23Na signals. An improved filter with better suppression of spurious 1Q 23Na signals is obtained by adding a preparatory crusher gradient and two-step phase cycling to a conventional GS3Q filter. The relative contributions of 3Q coherence and spurious 1Q coherences to the conventional and modified-GS3Q-filtered signals are calculated, providing a measure of the effectiveness of each GS3Q filter. The filters were implemented on a 2.35 T medium-bore spectrometer and their predicted properties verified. SNR measurements from GS3Q-filtered three-dimensional images of an agarose gel phantom indicate that 0.012 M23Na images in the human brain can be acquired with 8 cm3 voxels and SNR of 10 in 30 minutes at 2.35 T, assuming similar relaxation times.