  The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1
dimensions is employed to study the effect of the Skyrme term on the
semiclassical analysis of a field theory with instantons. The instantons of
this model are self-dual and can be evaluated explicitly. They are also
localised to an absolute scale, and their fluctuation action can be reduced to
a scalar subsystem. This permits the explicit calculation of the fluctuation
determinant and the shift in vacuum energy due to instantons. The model also
illustrates the semiclassical quantisation of a Skyrmed field theory.
