We derive astrophysical and structural parameters of the poorly studied open clusters NGC 6866, NGC 7062, and NGC 2360 based on filtered 2MASS (J,J - H) diagrams, and stellar radial density profiles. The field star decontamination technique is utilised for selecting high-probability cluster members. The E(B - V) reddening values of the three clusters derived from 2MASS JHK(s), agree with those inferred from UBV and uvby - beta photometries. We find that the core mass function slopes are flatter than the halo's for the three clusters. The large core and cluster radii of NGC 6866 and NGC 2360 indicate an expanded core, which may suggest the presence of stellar mass black-holes. NGC 2360 is located in the third quadrant (l = 229 degrees.80), where Giant Molecular Clouds are scarce that, together with its relatively large mass (similar to 1800 m(circle dot)), might explain its longevity (similar to 1.8 Gyr) in the Galaxy. (C) 2012 Elsevier B.V. All rights reserved.