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We present high contrast images of the hydrogen white dwarf G 29-38 taken inthe near infrared with the Hubble Space Telescope and the Gemini NorthTelescope as part of a high contrast imaging search for substellar objects inorbit around nearby white dwarfs.  We review the current limits on planetary companions for G29-38, the onlynearby white dwarf with an infrared excess due to a dust disk. We add ourrecent observations to these limits to produce extremely tight constraints onthe types of possible companions that could be present. No objects $>$ 6M$_{Jup}$ are detected in our data at projected separations $>$ 12 AU, and noobjects $>$ 16 M$_{Jup}$ are detected for separations from 3 to 12 AU, assuminga total system age of 1 Gyr. Limits for companions at separations $<$ 3 AU comefrom a combination of 2MASS photometry and previous studies of G29-38'spulsations. Our imaging with Gemini cannot confirm a tentative claim for thepresence of a low mass brown dwarf. These observations demonstrate that acareful combination of several techniques can probe nearby white dwarfs forlarge planets and low mass brown dwarfs.Comment: 20 pages, 4 figures, Accepted to Ap

Cool Customers in the Stellar Graveyard. I. Limits to Extrasolar Planets Around the White Dwarf G29‐38