Using a state-of-the-art full-potential electronic structure method within the local spin density approximation, we study the electronic and magnetic structure of Mn₂V-based full Heusler alloys: Mn₂VZ (Z=Al,Ga,In,Si,Ge and Sn. We show that small expansion of the calculated theoretical equilibrium lattice constants restores the half-metallic ferrimagnetism in these compounds. Moreover, a small degree of disorder between the V and Z atoms, although it induces some states within the gap, preserves the Slater-Pauling behavior of the spin magnetic moments and the alloys keep a high degree of spin polarization at the Fermi level, opening the way for a half-metallic compensated ferrimagnet.