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Structural and dynamical parameters of faint open clusters are probed withquality 2MASS-photometry and analytical procedures developed for brightclusters. We derive fundamental parameters of the faint open clusters Lynga2,BH63, Lyng12 and King20, the last three of which have no prior determinations.We also focus on the structure and dynamical state of these clusters. 2MASSphotometry with errors smaller than 0.2mag are used to build CMDs, RDPs, CMDs,luminosity and mass functions. Colour-magnitude filters are used to isolateprobable member stars. Field-star decontamination is applied to Lynga2, Lynga12and King20. Reddening values are in the range 0.22-1.9, with BH63 the mostreddened object. Ages of Lynga2, King20, Lynga12 and BH63 are ~90, ~200, ~560and 700Myr, respectively. The RDPs of Lynga12 and King20 are well-representedby King profiles. Total stellar masses (extrapolating the MFs to stars with0.08Mo) range from ~340Mo (BH63) to ~2300Mo (Lynga12). Observed masses are\~1/4$ of these values. In all clusters the core mass function is flatter thanthe halo's. Faint open clusters can be probed with 2MASS when associated withcolour-magnitude filters and field-star decontamination. BH63 appears to be inan advanced dynamical state, both in the core and halo. To a lesser degree thesame applies to King20. Marginal evidence of dynamical evolution is present inthe cores of Lynga2 and Lynga12.Comment: 11 pages, 8 figures. Astronomy & Astrophysics, accepted, 04/09/200

Faint open clusters with 2MASS: BH 63, Lyngå 2, Lyngå 12 and King 20