This paper discusses methods for reconstructing the tongue from sparse data sets. Sixty ultrasound slices already have been used to reconstruct three-dimensional (3D) tongue surface shapes [Stone and Lundberg, J. Acoust. Soc. Am. 99, 3728-3737 (1996)]. To reconstruct 3D surfaces, particularly in motion, collecting 60 slices would be impractical, and possibly unnecessary. The goal of this study was to select a sparse set of slices that would best reconstruct the 18 measured speech sounds. First a coronal sparse set was calculated from 3D surface reconstructions. Selection of contours was globally optimized using coarse to fine search. Sparse and dense reconstructions were compared using maximum error, standard deviation error, and surface coverage. For all speech sounds, maximum error was less than 1.5 mm, standard deviation error was less than 0.32 mm, and average reconstruction coverage was 80%. To generalize the method across subjects, optimal slice locations were calculated from only the midsagittal contour. Six midsagittal points were optimized to reconstruct the midsagittal contour. Corresponding coronal slices were then used to reconstruct 3D surfaces. For data collection planning, a midsagittal sample can be collected first and optimal coronal slices can be determined from it. Errors and reconstruction coverage from the midsagittal source set were comparable to the optimized coronal sparse set. These sparse surfaces reconstructed static 3D surfaces, and should be usable for motion sequences as well.