It has become common practice to measure ocean current velocities together with the hydrography by lowering an ADCP on typical CTD casts. The velocities and densities thus observed are considered to consist mostly of a background contribution in geostrophic balance, plus internal waves and tides. A method to infer the geostrophic component by inverting the linearized potential vorticity (Pv) provides plausible geostrophic density and velocity distributions. The method extracts the geostrophic balance closest to the measurements by minimizing the energy involved in the difference, supposed to consist of Pv-free anomalies. The boundary conditions and the retention of Pv by the geostrophic estimates follow directly from the optimization, which is based on simple linear dynamics and avoids both the use of the thermal wind equation on the measured density, and the classical problem of a reference velocity. By construction, the transport in geostrophic balance equals the measured one. Tides are the largest source of error in the calculation. The method is applied to six ADCP/CTD surveys made across the Yucatan Channel in the springs of 1997 and 1998 and in the winter of 1998-1999. Although the time interval between sections is sometimes close to one inertial period, large variations on the order of 10 percent are found from one section to the next. Transports range from 20 to 31 Sv with a net average close to 25 Sv, consisting of 33 Sv of inflow into the Gulf of Mexico and 8 Sv of outflow into the Caribbean Sea. The highest velocities are 2.0 m sec-1 into the Gulf of Mexico near the surface on the western side of the channel, decreasing to 0.1 m sec-1 by 400 to 500 m depth. Beneath the core of the Yucatan Current a countercurrent, with speeds close to 0.2 m sec-1 and an average transport of 2 Sv, hugs the slopes of the channel from 500 to 1500 m depth. Our data show an additional 6 Sv of return flow within the same depth range over the abrupt slope near Cuba, which is likely to be the recirculating fraction of the Yucatan Current deep extention, unable to outflow through the Florida Straits. The most significant southerly flows do not occur in the deepest portion of the channel, but at depths around 1000 m.