Some communication systems embed pilot tones into the data spectrum to aid the receiver in synchronization, which may result in a DC offset of the baseband data. This paper motivates the use for adaptive estimation of the DC offset at the receiver, and proposes a Constant Modulus cost function that is jointly minimized over the DC offset estimate and the equalizer parameters. It is shown that for an arbitrary DC offset, the CM cost function admits local spurious minima in terms of equalizer settings, and that matching the DC offset at the receiver to the level inserted at the transmitter causes both local and global minima in terms of equalizer settings. Extrema of the cost function in terms of a DC offset are derived and classified, and adaptive methods for DC offset estimation are introduced.