  The apparent lack of suitable astrophysical sources for the observed highest
energy cosmic rays (UHECRs) within $\approx 20$ Mpc is the "GZK Paradox". We
constrain representative models of the extra-galactic magnetic field structure
by Faraday Rotation measurements; limits are at the $\mu$G level rather than
the nG level usually assumed. In such fields, even the highest energy cosmic
rays experience large deflections. This allows nearby AGNs (possibly quiet
today) or GRBs to be the source of ultra-high energy cosmic rays without
contradicting the GZK distance limit.
