expenditures to release the envelope (blue dashed line, see also the caption of Fig.\[alpha\]). Black solid and dotted lines indicate possible final binary configurations, assuming angular momentum lost in accordance with the $\gamma$-formalism, where thick black solid lines show minimum and maximum $\gamma$ that make a physically viable binary, and dotted black lines show values of $\gamma$ that lead to formation of physical viable binaries for all range of the core masses. Other lines’ styles are as in Fig.\[alpha\]. \[gamma1\] ](fig_gamma1.eps){height=".36\textheight"}

As we indicated, the consistency of the solution considered above is coincidental. We will now consider two examples where a CE with $\gamma \approx 1.5$ does not lead to a self-consistent solution.

First, we take the same $2\,M_\odot$ giant with the same $m_\mathrm{c, min}\sim 0.4\,M_\odot$, but with a $1.5\,M_\odot$ companion (Fig.\[gamma2\]), similar to some initial binaries considered to be progenitors for DWDs in [@Sluys2006], and consider how the $\gamma$ formalism treats the first phase of MT here. This binary would have a self-consistent post-CE binary separation only for $\gamma\approx1.99-2.06$ (close to values of $\gamma$ used in some similar systems in [@Sluys2006], see their Table 6). With $\gamma=1.5$, this binary would extract too little angular momentum to remain an energy-consistent 