The goal is to quantify in an eddy-rich ocean environment the accuracy of currents obtained from a multi-level primitive-equation ocean model that assimilates altimetry sea-surface height anomaly (SSHA) and surface drifters. The 1999-2000 period in the Gulf of Mexico is chosen for the availability of drifters and Acoustic Doppler Current Profiler (ADCP) measurements in the loop current and eddies during that period. Sequential assimilations of SSHA and/or currents with statistical-interpolation schemes are used. Experiments initialized with and without altimetry and/or drifter assimilations, including a forecast case (without assimilation) for comparison, are conducted. It is shown that the SSHA + Drifter analysis consistently outperforms the analysis that assimilates only SSHA, especially at smaller scales. Drifter-assimilation alone also constraints the pressure field, such that the loop and eddies compare quite favorably with altimetry SSH field. When compared against independent ADCP data, the analyses with either SSHA or SSHA + Drifter assimilation yield amplitude and phase of analysis-to-observed complex (velocity) correlation of 0.76-0.86 and 0.3°-7°, respectively. The mean speed and direction (absolute) errors are 0.4-5 cm s-1 (1-10% errors) and 10°-20°, respectively. The correlations of the two dominant empirical orthogonal function (EOF) modes with the corresponding observation modes at a yearlong mooring over the northern slope are: mode-1 ≈ 0.88-0.93 and mode-2 ≈ 0.5-0.63. Both show vertically coherent but strongly sheared modes 1 and 2 representing propagation eddies and reversing mode-3 that intensifies for z < -300 m.