  Phase-resolved spectroscopy of four AM CVn systems obtained with the William
Herschel Telescope and the Gran Telescopio de Canarias (GTC) is presented.
SDSS\,J120841.96+355025.2 was found to have an orbital period of
52.96$\pm$0.40\,min and shows the presence of a second bright spot in the
accretion disc. The average spectrum contains strong Mg\,{\sc i} and Si\,{\sc
i/ii} absorption lines most likely originating in the atmosphere of the
accreting white dwarf. SDSS\,J012940.05+384210.4 has an orbital period of
37.555$\pm$0.003 min. The average spectrum shows the Stark broadened absorption
lines of the DB white dwarf accretor. The orbital period is close to the
previously reported superhump period of 37.9\,min. Combined, this results in a
period excess $\epsilon$=0.0092$\pm$0.0054 and a mass ratio $q=0.031\pm$0.018.
SDSS\,J164228.06+193410.0 displays an orbital period of 54.20$\pm$1.60\,min
with an alias at 56.35\,min. The average spectrum also shows strong Mg\,{\sc i}
absorption lines, similar to SDSS\,J120841.96+355025.2.
SDSS\,J152509.57+360054.50 displays an period of 44.32$\pm$0.18\,min. The
overall shape of the average spectrum is more indicative of shorter period
systems in the 20-35 minute range. The accretor is still clearly visible in the
pressure broadened absorption lines most likely indicating a hot donor star
and/or a high mass accretor. Flux ratios for several helium lines were
extracted from the Doppler tomograms for the disc and bright spot region, and
compared with single-slab LTE models with variable electron densities and path
lengths to estimate the disc and bright spot temperature. A good agreement
between data and the model in three out of four systems was found for the disc
region. All three systems show similar disc temperatures of $\sim$10\,500 K. In
contrast, only weak agreement between observation and models was found for the
bright spot region.
