From August 1993 to October 1994, Magellan was at heights 180 to 550 km. Products of the Deep Space Network (DSN) X band tracking are line-of-sight (LOS) Doppler frequencies and accelerations residual to a 40th degree gravity field. The intrinsic accuracy and abundance of these data may be good enough to push the resolution (half wavelength) to less than spacecraft height. The observation equation to infer gravity from LOS accelerations is simple. However, noise and non uniform geometry necessitate a singular value analysis cutoff or an a priori weighting; the latter was chosen for computational economy. Further, the non-Gaussian character of the noise necessitates a reject limit. Choices made were: (1) surface element size 100 km; (2) region size 1600 km; (3) buffer zone width 600 km; (4) reject limit 1 mGal (10-5 m/s); and (5) criterion for a priori weighting recovering a known solution; i.e., a field transferred from Earth to Venus (probably the most significant technical advance). This criterion was optimized by a priori increments to the normal main diagonal about 10% of the minimum main diagonal element, averaging about 0.5% of the maximum. Best resolutions, defined by spectral coherence of 0.7 for the known field, obtained were 110 km near the equator (from 51,285 points over Eisila) and 180 km at high latitudes (from 120,231 points over Maxwell and 162,000 over Akna/Freyja). The limitation on resolution near the equator is the cubic polynomial fitting over 335 km lengths to determine accelerations. However, environmental effects were the limiters elsewhere. Root-mean-square (rms) residuals to solutions had negative correlations with spacecraft altitude and the angle at the Earth between Venus and the Sun, and positive correlations with the Earth-Venus distance and latitude on Venus, indicating Venus's influence on its electromagnetic surroundings out to several 100 km, especially on its side toward the Sun. Correlations with DSN zenith angles and the Kp index of solar activity were positive, but slight. The main characteristic of the enhanced resolution of regional gravity fields is greater correlation with the topography at shorter wavelengths. The main improvement yet to be made is to generate a full a priori matrix of the regional gravity field. ¿ American Geophysical Union 1995