Top: relation between velocity dispersion σ_⋆ and difference between M_BH estimates from σ_⋆ using the scaling law of McConnell et al. (2011) and the scaling law from VP. The shaded area identifies the range of σ_⋆ ≤ 160 km s⁻¹ . All data points, save one yielding large systematic differences (> 0.4, represented with open squares) with respect to the VP M_BH, are within the shaded area. Bottom: same as in the top panel, but with the M_BH values computed with the correction described in Sect. 5.4.