Adiabatic soliton compression is an attractive optical pulse compression scheme that relies on monotonic decreasing of the fiber dispersion along the soliton's propagation path. This scheme requires kilometers of specialty fiber, and only a few dispersion profiles are practically feasible. We propose adiabatic soliton compression in a nonuniform fiber Bragg grating. The Bragg soliton propagates in the passband of a grating, where one or more of its parameters (e.g., the grating pitch) varies along the propagation direction. - The capability of manufacturing almost arbitrary grating profiles and hence engineering practically any dispersion profile makes this all-fiber pulse compressor, which is to our knowledge novel, a very versatile component. Additionally, the large dispersion in the spectral vicinity of the grating stop band leads to Very short devices (tens of centimeters as opposed to kilometers). (C) 1998 Optical Society of America [S0740-3224(98)02112-2] OCIS codes: 320.0320, 320.5520, 060.5530, 060.4370, 320.7110, 230.1480, 060.2340.