  We present new results for the current as a function of transmission rate in
the one dimensional totally asymmetric simple exclusion process (TASEP) with a
blockage that lowers the jump rate at one site from one to r < 1. Exact finite
volume results serve to bound the allowed values for the current in the
infinite system. This proves the existence of a gap in allowed density
corresponding to a nonequilibrium ``phase transition'' in the infinite system.
A series expansion in r, derived from the finite systems, is proven to be
asymptotic for all sufficiently large systems. Pade approximants based on this
series, which make specific assumptions about the nature of the singularity at
r = 1, match numerical data for the ``infinite'' system to a part in 10^4.
