In many cases where direction finding is of interest, the signals impinging on an antenna array are known to be phase modulated and, hence, to have a constant modulus (CM). This is a strong property; by itself, it is already sufficient for source separation and can be used to construct improved direction finding algorithms. We first derive the relevant Cramer-Rao bounds (CRBs) for arbitrary array configurations and specialize to uniform linear arrays. We then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the CM property followed by direction finding on the decoupled signals. Compared with the ESPRIT algorithm and the CRB for arbitrary signals, the algorithm shows good results.