Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Generally these gradients are not modeled in standard very long baseline interferometry (VLBI) geodetic analysis. Daily average gradient effects can be as large as 50 mm of delay at a 7¿ elevation. To model gradients, the constrained estimation of gradient parameters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990--1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990--1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties. ¿ American Geophysical Union 1995