  We study fundamental and compound gap solitons (GSs) of matter waves in
one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D)
weak-radial-confinement regime, which corresponds to realistic experimental
conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit
nontrivial radial structures. Associated with each 3D linear spectral band
exists a family of fundamental gap solitons that share a similar transverse
structure with the Bloch waves of the corresponding linear band. GSs with
embedded vorticity $m$ may exist \emph{inside} bands corresponding to other
values of $m$. Stable GSs, both fundamental and compound ones (including vortex
solitons), are those which originate from the bands with lowest axial and
radial quantum numbers. These findings suggest a scenario for the experimental
generation of robust GSs in 3D settings.
