  The height of a random PATRICIA tree built from independent, identically
distributed infinite binary strings with arbitrary diffuse probability
distribution $\mu$ on $\{0,1\}^\mathbb{N}$ is studied. We show that the
expected height grows asymptotically sublinearly in the number of leaves for
any such $\mu$, but can be made to exceed any specific sublinear growth rate by
choosing $\mu$ appropriately.
