  We describe a general way of constructing integrable defect theories as
perturbations of conformal field theory by local defect operators. The method
relies on folding the system onto a boundary field theory of twice the central
charge. The classification of integrable defect theories obtained in this way
parallels that of integrable bulk theories which are a perturbation of the
tensor product of two conformal field theories. These include local defect
perturbations of all $c<1$ minimal models, as well as of the coset theories
based on SO(2n), obtained in this way. We discuss in detail the former case of
all the Virasoro minimal models. In the Ising case our construction corresponds
to having a spin field as a defect operator; in the folded formulation this is
mapped onto an orbifolding of the boundary sine-Gordon theory at $\beta^2/8\pi
= 1/8$, or a version of the anisotropic Kondo model.
