We construct a simple field theory in which a sphaleron, i.e., a saddle-point
particle-like solution, forms a semi-BPS state with a background defect that is
an impurity. This means that there is no static force between the sphaleron and
the impurity. Therefore such a sphaleron-impurity system is very much like
usual BPS multi-solitons, however, still possessing an unstable direction
allowing for its decay. We study dynamics of the sphaleron in such a system.Comment: 13 pages, 12 figures, references added and improved discussio