  Common-envelope phases are decisive for the evolution of many binary systems.
Of particular interest are cases with asymptotic giant branch (AGB) primary
stars, because they are thought to be progenitors of various astrophysical
transients. In three-dimensional hydrodynamic simulations with the moving-mesh
code AREPO, we study the common-envelope evolution of a $1.0\,M_{\odot}$
early-AGB star with companions of different masses. Although the stellar
envelope of the AGB star is less tightly bound than that of a red giant, we
find that the release of orbital energy of the core binary is insufficient to
eject more than about twenty percent of the envelope mass. Ionization energy
released in the expanding envelope, however, can lead to complete envelope
ejection. Because recombination proceeds largely at high optical depths in our
simulations, it is likely that this effect indeed plays a significant role in
the considered systems. The efficiency of mass loss and the final orbital
separation of the core binary system depend on the mass ratio between the
companion and the primary star. Our results suggest a linear relation between
the ratio of final to initial orbital separation and this parameter.
