Electron density measurements of six coronal bright points have been obtained using line ratio diagnostics of four ions in the temperature range 1.3-2.0 × 106 K. The results suggest that BP plasma has more similarities to active region plasma than to quiet Sun plasma. Nevertheless, they do not show the exact same behaviour: the increase of electron density at temperatures over log~Te ~ 6.2, observed in the core of active regions, has not been detected. The Fe XII results based on new atomic data, although in better agreement decreasing more than a factor of two the densities obtained with older calculations, are still in some instances higher than those from Si X. This could be a consequence of the inhomogeneity of the plasma in the observed volume. New measurements with a better constriction of the volumetric properties seem necessary to rule out the influence of other factors and confirm whether there is an inconsistency between the ions, perhaps due to line blending problems in the Fe XII lines.