  We completed observations with the Effelsberg 100-m radio telescope to
measure the polarised emission from a complete sample of Compact Steep-Spectrum
sources. We observed the sources at four different frequencies. We complemented
these measurements with polarisation parameters at 1.4 GHz derived from the
NVSS. Previous single dish measurements were taken from the catalogue of Tabara
and Inoue. The depolarisation index DP was computed for four pairs of
frequencies. A drop in the fractional polarisation appeared in the radio
emission when observing at frequencies below about 2 GHz. Rotation measures
were derived for about 25% of the sources in the sample. The values range from
about -20 rad/m**2} found for 3C138 to 3900 rad/m**2 in 3C119. In all cases,
the lambda**2 law is closely followed. The presence of a foreground screen as
predicted by the Tribble model or with ``partial coverage'' as defined by
ourselves can explain the polarimetric behaviour of the CSS sources detected in
polarisation by the present observations. Indication of repolarisation at lower
frequencies was found for some sources. A case of possible variability in the
fractional polarisation is also suggested. The most unexpected result was found
for the distribution of the fractional polarisations versus the linear sizes of
the sources. Our results appear to disagree with the findings of Cotton and
collaborators and Fanti and collaborators for the B3-VLA sample of CSS sources,
the so-called ``Cotton effect''. This apparent contradiction may, however, be
caused by the large contamination of the sample by quasars with respect to the
B3-VLA.
