Numerous correlations of one-way reflection travel times and depths to reflecting horizons have been proposed in the Initial Reports of the Deep Sea Drilling Project (DSDP). Having carefully reviewed proposed correlations, we selected 233 correlated depths (ranging from 27 m to 1.4 km) and one-way travel times (ranging from 0.02 to 0.7 s) from 154 DSDP sites worldwide. Assuming that the velocity/depth function for deep-sea sediments can be approximated by an exponential form, we have used these data to establish statistically well-constrained global models relating depth to travel time and velocity to depth. There is remarkably little scatter in the data. Based on nonlinear least squares fits, the best depth/time function is Z(km)=-3.03 ln<1-0.52T(s)>; the rms error in depth is 26 m. The corresponding average velocity/depth function is V(km/s)=1.59exp(0.33Z). We estimate that the real site-to-site variability of velocities at depth is less than 0.20 km/s. Any dependence of velocity on composition is below the resolution of the data, and available evidence suggests that age has no significant effect. These results imply that to a depth of 1.4 km the physical state of sediments depends on in situ overburden pressure and temperature, which are related to depth of burial, and that chemical and mechanical equilibrium is achieved in a period of time that is geologically short. Our results are consistent with laboratory measurements of P wave velocities in deep-sea sediments, but velocity/depth functions for terrigenous and calcareous sections derived from sonobuoy wide-angle reflection surveys are incompatible with the time and depth data, and overestimate velocities by as much as 10% and 30%, respectively. These systematic errors may result from the fact that the marked anisotropy of deep-sea sediments is neglected in the interpretation of reflection data.