Several interesting features of coset models ''without fixed points''
are easily understood via Chern-Simons theory. In this paper we derive
explicit formulae for the handle-squashing operator in these cosets.
These operators are fixed, linear combinations of the irreducible repr
esentations of the coset. As a simple application of these curious for
mulae, we compute the traces of all genus-one operators for several co
mmon cosets.