  We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie
algebra to the usual ones by a very elementary approach. The comparison gives
some conditions, which are easy to verify for a given Lie algebra, for deciding
whether it has more Leibniz deformations than just the Lie ones. We also give
the complete description of a Leibniz (and Lie) versal deformation of the
4-dimensional diamond Lie algebra, and study the case of its 5-dimensional
analogue.
