  We quantize the exterior of spherically symmetric vacuum space-times using a
midi-superspace reduction within the Ashtekar new variables. Through a partial
gauge fixing we eliminate the diffeomorphism constraint and are left with a
Hamiltonian constraint that is first class. We complete the quantization in the
loop representation. We also use the model to discuss the issues that will
arise in more general contexts in the ``uniform discretization'' approach to
the dynamics.
