We show that a rotating-compensator ellipsometer (RCE) with a zero-order retarder can be used for broadband spectroscopy, for example from 200 to 800 nm, when the compensator retardation delta is known as a function of wavelength and sample properties are determined by least-squares methods. The resulting instrument offers the standard advantages of an RCE and is no less sensitive than a rotating-analyzer or -polarizer ellipsometer under worst-case conditions, where the sin (2 omega t) component vanishes at delta=180 degrees C. Sensitivity and operation are illustrated by application to the measurement of crystalline Si.