The average degree of a multigraph critical with respect to edge or total choosability

Let GG be a multigraph with maximum degree at most Δ⩾3Δ⩾3 such that ch′(G)>Δ or ch″(G)>Δ+1 and GG is minimal with this property. A new proof is given for the result (which was already known, apart from a simple calculation) that the average degree of GG is greater than 2Δ except possibly in the second case when Δ=5Δ=5.