  Following a brief review of the principles of the strong equivalence
principle (SEP) and tests for its violation in the strong and weak
gravitational field regimes, we present preliminary results of new tests using
two long-period binary pulsars: J0407+1607 and J2016+1947. PSR J0407+1607 is in
a 669-day orbit around a $\gapp 0.2$ M$_{\odot}$ companion, while J2016+1947 is
in a 635-day orbit around a $\gapp 0.3$ M$_{\odot}$ companion. The small
eccentricities of both orbits ($e \sim 10^{-3}$) mean that these systems reduce
previous limits on SEP violation by more than a factor of 4.
