  We provide a rationale for a new class of double-hybrid approximations
introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which
combine an exchange-correlation density functional with Hartree-Fock exchange
weighted by $\l$ and second-order M{\o}ller-Plesset (MP2) correlation weighted
by $\l^3$. We show that this double-hybrid model can be understood in the
context of the density-scaled double-hybrid model proposed by Sharkas et al.
[J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled
correlation functional $E_c[n_{1/\l}]$ by a linear function of $\l$,
interpolating between MP2 at $\l=0$ and a density-functional approximation at
$\l=1$. Numerical results obtained with the Perdew-Burke-Ernzerhof density
functional confirms the relevance of this double-hybrid model.
