  Factorization of string amplitudes is one way of constructing string
interaction vertices. We show that correlation functions in string theory can
be conveniently factorized using loop variables representing delta functionals.
We illustrate this construction with some examples where one particle is
off-shell. These vertices are ``correct'' in the sense that they are
guaranteed, by construction, to reproduce S-matrix elements when combined with
propagators in a well defined way.
