  We have carried out multicolour imaging of a complete sample of radio-loud
quasars at 0.6 < z < 1.1 and find groups or clusters of galaxies in the fields
of at least 8 and possibly 13 of the 21 sources. There is no evidence for an
evolution in the richness of the environments of radio-loud quasars from other
low-redshift studies to z >~ 0.9. The quasars associated with groups and
clusters in our sample do not necessarily reside in the centre of the galaxy
distribution which rarely displays a spherical geometry. Clustering is
preferentially associated with small or asymmetric steep-spectrum radio
sources. The quasars with the largest projected angular size are, in nearly all
cases, found in non-clustered environments. Radio-based selection (including
source size) of high-redshift groups and clusters can be a very efficient
method of detecting rich environments at these redshifts.
  We find that in optical searches for galaxy overdensities above z ~ 0.6
multiple filters must be used. If the single-filter counting statistics used by
groups at lower redshift are applied to our data, uncertainties are too large
to make accurate quantifications of cluster richness. This means that genuine
clustering of galaxies about quasars will be missed and, in ~10% of cases,
putative clusters turn out to be false detections. The statistics are further
diluted by the fact that galaxy overdensities are generally not centred on the
quasar.
