  It has recently been demonstrated that certain types of non-tensional
stress-energy can live on tensional codimension-2 branes, including
gravitational shockwaves and small Schwarzschild black holes. In this note we
generalize the earlier Schwarzschild results, and construct the exact
gravitational fields of small rotating black holes on a codimension-2 brane. We
focus on the phenomenologically interesting case of a three-brane embedded in a
spacetime with two compactified extra dimensions. For a nonzero tension on the
brane, we verify that these solutions also show the ``lightning rod'' effect
found in the Schwarzschild solutions, the net effect of which is to rescale the
fundamental Planck mass. This allows for larger black hole parameters, such as
the event horizon, angular momentum, and lifetime than would be naively
expected for a tensionless brane. It is also found that a black hole with
angular momentum pointing purely along the brane directions has a smaller
horizon angular velocity than the corresponding tensionless case, while a hole
with bulk components of angular momentum has a larger angular velocity.
