Context : Structural parameters and the total M _ { V } magnitude are important properties to be used in the characterization of individual globular clusters .
With the increasing statistics , especially of the intrinsically faint objects , collective properties of the Galactic globular cluster system will be better defined , with reflexes on our understanding of the formation history of the Galaxy .

Aims : 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 IC 1257 , Lyngå 7 , Terzan 4 , Terzan 10 , BH 176 , ESO 452-SC11 , ESO 280-SC08 , 2MASS-GC01 , 2MASS-GC02 , GLIMPSE-C01 and AL 3 , which are projected not far from the central region of the Galaxy .
Field-star contamination is significant in the colour-magnitude diagrams .
Half of the sample have an absorption \mbox { $A _ { V } $ } \ga 7 , reaching in some cases \mbox { $A _ { V } $ } \ga 15 .

Methods : 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 , so an algorithm that we previously developed for open clusters in rich fields is employed to better define cluster sequences .
With decontaminated photometry we also compute the total M _ { V } of four such globular clusters , using M 4 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 .

Results : Compared to massive globular clusters , those in the present sample have smaller tidal and larger core radii for a given Galactocentric distance , which is consistent with rather loose structures .
Globular cluster radii derived from number-density and surface-brightness profiles have similar values .
The present magnitude estimates are \mbox { $M _ { V } $ } \approx - 4.9 ( ESO 280-SC08 ) , \mbox { $M _ { V } $ } \approx - 5.8 ( 2MASS-GC01 ) and \mbox { $M _ { V } $ } \approx - 5.6 ( 2MASS-GC02 ) .
We also estimate \mbox { $M _ { V } $ } \approx - 6.1 for GLIMPSE-C01 , which results somewhat less luminous than previously given .
The density profiles of Tz 4 and 2MASS-GC01 present evidence of post-core collapse clusters .

Conclusions : 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 .