  We discuss generalized baby Skyrmions emerging in a (1+2)-dimensional
$\sigma$ model with a certain Lie-algebraic structure. The same result applies
to the Polyakov-Belavin instantons in $D=1+1$. The O(3) symmetry of the target
space is lost, but O(2) is preserved in the simplest model under consideration.
Both the topological charge and the soliton mass (the instanton action) are
determined. Of special interest are limiting cases of the deformation parameter
$k$ (also referred to as the elongation parameter). If $|k-1|\ll 1$, we arrive
at a model which is studied in condensed matter. If $k\gg1$, we obtain the
so-called cigar, or sausage model, well-known in little string theory. If
$k=1$, we return to CP(1). The deformed model under consideration interpolates
between CP(1) and the cigar model. In $D=2$ we calculate the coupling constants
renormalization at one loop. At $k\geq 1$ this class of models is
asymptotically free in the ultraviolet limit and enters the strong coupling
domain in the infrared. Also, in the infrared $k\to 1$ (i.e., we recover
CP(1)).
