  We observed in our previous paper that all the complex structures on
four-dimensional compact solvmanifolds, including tori, are left-invariant. In
this paper we will give an example of a six-dimensional compact solvmanifold
which admits a continuous family of non-left-invariant complex structures.
Furthermore, we will make a complete classification of three-dimensional
compact homogeneous complex solvmanifolds; and determine which of them admit
pseudo-Kaehler structures.
