  The determination of structural parameters of 11 faint Galactic globular
clusters that, in most cases, had not been previously studied in this context.
The clusters are IC1257, Lynga7, Terzan4, Terzan10, BH176, ESO452-SC11,
ESO280-SC08, 2MASS-GC01, 2MASS-GC02, GLIMPSE-C01 and AL3, which are projected
not far from the central region of the Galaxy. Field-star contamination is
significant in the colour-magnitude diagrams. Stellar radial number-density and
surface-brightness profiles are built with 2MASS photometry that, for the
present clusters, corresponds basically to giant-branch stars. Field-star
decontamination is essential for clusters in dense fields. With decontaminated
photometry we also compute the total MV of four such globular clusters, using
M4 as a template. King-like functions are fitted to the radial profiles, from
which the core, half-light, half-star count and tidal radii are derived,
together with the concentration parameter. Parameters derived here are compared
to the equivalent ones of other Galactic globular clusters available in the
literature. Structural parameters and luminosity of most of the faint globular
clusters dealt with in this paper are consistent with those of Palomar-like
(low-mass and loose structure) globular clusters. This work helps to improve
coverage of the globular cluster parameter space.
