Compressional-wave velocities have been measured for propagation directions parallel and perpendicular to bedding in 11 calcareous deep sea sediments at confining pressures to 1.0 kbar. The samples, recovered from subbottom depths of 0.39--0.75 km in the western South Atlantic on DSDP leg 39, range in wet bulk density from 1.83 to 2.30 g/cm-3 and in porosity from 23 to 48%. The sediments exhibit significant velocity anisotropy at all pressures, with velocities in the bedding plane higher than those measured in the vertical direction. At 0.1 kbar, horizontal velocities (Vh) range from 1.80 to 2.99 km/s, while vertical velocities range 1.65 to 2.54 km/s. Corresponding ranges of ΔV= (Vh-Vv) and anisotropy (A=2(Vh-Vv)/(Vh+Vv)) are 0.10--0.45 km/s and 5.2--16.3%, respectively. Both ΔV and A increase markedly with depth of burial: ∂ΔV/∂z=0.62 km/s/km, and ∂A/∂z=19%/km. The failure of anisotropy to decrease with increasing confining pressure suggests that this phenomenon is not produced by the alignment of cracks. However, the elastic properties of calcite are such that an alignment of c axes perpendicular to bedding would produce the observed velosity distribution. Suggested mechanisms for producing the fabric are: (1) the alignment of certain microfossils such as Discoaster during compaction, (2) epitaxial growth of aligned forms during diagenesis, and (3) recrystallization of calcite.