Abstract In weakly indurated, nannofossil-rich, deep-sea carbonates compressional wave velocity is up to twice as fast parallel to bedding than normal to it. It has been suggested that this anisotropy is due to alignment of calcite c-axes perpendicular to the shields of coccoliths and shield deposition parallel to bedding. This hypothesis was tested by measuring the preferred orientation (fabric) of calcite c-axes in acoustic anisotropic, calcareous DSDP sediment samples by X-ray goniometry, and it was found that the maximum c-axis concentrations are by far too low to explain the anisotropies. The X-ray method is subject to a number of uncertainties due to preparatory and technical shortcomings in weakly indurated rocks. The most serious weaknesses are: sample preparation, volume of measured sample (fraction of a mm 3), beam defocusing and background intensity corrections, combination of incomplete pole figures, and necessity of recalculation of the c-axis orientations from other crystallographic directions. Goniometry using thermal neutrons overcomes most of these difficulties, but it is time consuming. We test the interferences made about velocity anisotropy by X-ray studies about the concentration of c-axes in deep-sea carbonates by employing neutron texture goniometry to eight DSDP samples comprising mostly nannofossil material. Fabric and sonic velocity were determined directly on the core specimens, thus from the same rock volume and requiring no preparation. The c-axis orientation is obtained directly from the  calcite diffraction peak without corrections. The fabrics are clearly defined, but weak (1.1 to 1.86 times uniform) with the maximum about normal to bedding. They have crudely orthorhombic symmetry, but are not axisymmetric around the bedding normal. The observed c-axis intensities, although higher than determined by the X-ray method on other samples, are by far too low to explain the observed acoustic anisotropies.