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 Mn$_2$V-based full Heusler alloys: Mn$_2$VZ (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 iduces some states within the gap, it preserves the Slater-Pauling behaviour of the spin magnetic moments and the alloys keep a high degree of spin-polarisation at the Fermi level opening the way for a half-metallic compensated ferrimagnet.