What unitary matrix models are not?

We report results of two investigations of the double-scaling equations for the unitary matrix models. First, the fixed area partition functions have all positive coefficients only for the first four critical points. This implies that the critical points at $k\ge5$ describe non-unitary continuum theories. Secondly, we examine a conjectured connection to branched polymers, but find that the scaling solutions of the unitary models do not agree with those of a particular model describing branched polymers.