  We say that a smooth algebraic group $G$ over a field $k$ is very special if
for any field extension $K/k$, every $G_K$-homogeneous $K$-variety has a
$K$-rational point. It is known that every split solvable linear algebraic
group is very special. In this note, we show that the converse holds, and
discuss its relationship with the birational classification of algebraic group
actions.
