  The exclusion statistics of two complementary sets of quasiparticles,
generated from opposite ends of the spectrum, are identified for Ising chains
with spin s=1/2,1. In the s=1/2 case the two sets are antiferromagnetic domain
walls (solitons) and ferromagnetic domains (strings). In the s=1 case they are
soliton pairs and nested strings, respectively. The Ising model is equivalent
to a system of two species of solitons for s=1/2 and to a system of six species
of soliton pairs for s=1. Solitons exist on single bonds but soliton pairs may
be spread across many bonds. The thermodynamics of a system of domains spanning
up to $M$ lattice sites is amenable to exact analysis and shown to become
equivalent, in the limit M -> infinity, to the thermodynamics of the s=1/2
Ising chain. A relation is presented between the solitons in the Ising limit
and the spinons in the XX limit of the s=1/2 XXZ chain.
