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This article gives several new insights on ellipsometers using photoelastic modulators. The assumption that the modulation has the form δ=δ0+A sin ωt is ruled out. In contrast, it is shown that the presence of higher harmonics in the modulation affects the measured signal. A new formalism is proposed to take this effect into account, and experimental evidences of its consistency and relevance are exposed. Using this multiple-harmonic model, ellipsometric measurements showed a dispersion four to five times less than using the conventional model. A new method is proposed to adjust the modulation amplitude during the measurements, by measuring the third harmonic of the signal. It is proven experimentally that this method actually improves the precision of phase-modulated ellipsometry. Other sources of errors are reviewed, such as multiple reflections in coherent light. A practical procedure to test whether a modulator is well adapted to ellipsometry is given. [ABSTRACT FROM AUTHOR]