A free-fall instrument, TOPS, measures vertical profiles of horizontal ocean velocity, conductivity and temperature. Profiling capability extends throughout the full water column (6000 db pressure limitation). Larger vertical wavelength (water depth > λ ≳ 20 m) velocity fluctuations are resolved by acoustically tracking TOPS relative to an array of bottom moored transponders. Shorter vertical wavelength velocity fluctuations (1000 m ≳ λ > 0.2 m) are resolved by an onboard acoustic velocimeter, which measures ocean velocity relative to the profiler. Motions of the profiler are monitored with a two-axis accelerometer and fluxgate compass. The instrument, data acquisition system and processing are described. In order to interpret the onboard velocimeter measurements, a planar, irrotational flow model is developed that describes the response of TOPS to an arbitrary oceanic shear profile. The model is verified using measured velocity and acceleration and by comparing oceanic velocity computed from the onboard velocimeter with that obtained from the acoustic tracking system. The two velocity profiles, smoothed with a 25 m half-width Gaussian filter, had a rms difference over a 1000 m depth interval of only 2 cm s−1. Accelerometer measurements, interpreted through the response model, are also used to obtain ocean velocity over wavelengths longer than 10 m. These estimates agree with those based on the velocimeter to within 1.5 cm s−1. Results of our model are compared with other models that describe similar free-fall dropsondes. In addition, TOPS measured velocities are compared with independent measurements taken with another profiler. The agreement found in these internal and external comparisons gives confidence in the accuracy of the TOPS model and the ability to obtain full water column high-resolution velocity profiles in the manner described.