  Ultracompact accreting binary systems each consist of a stellar remnant
accreting helium-enriched material from a compact donor star. Such binaries
include two related sub-classes, AM CVn-type binaries and helium cataclysmic
variables, in both of which the central star is a white dwarf. We present a
spectroscopic and photometric study of six accreting binaries with orbital
periods in the range of 40--70 min, including phase-resolved VLT spectroscopy
and high-speed ULTRACAM photometry. Four of these are AM CVn systems and two
are helium cataclysmic variables. For four of these binaries we are able to
identify orbital periods (of which three are spectroscopic). SDSS J1505+0659
has an orbital period of 67.8 min, significantly longer than previously
believed, and longer than any other known AM CVn binary. We identify a WISE
infrared excess in SDSS J1505+0659 that we believe to be the first direct
detection of an AM CVn donor star in a non-direct impacting binary. The mass
ratio of SDSS J1505+0659 is consistent with a white dwarf donor. CRTS
J1028-0819 has an orbital period of 52.1 min, the shortest period of any helium
cataclysmic variable. MOA 2010-BLG-087 is co-aligned with a K-class star that
dominates its spectrum. ASASSN-14ei and ASASSN-14mv both show a remarkable
number of echo outbursts following superoutbursts (13 and 10 echo outbursts
respectively). ASASSN-14ei shows an increased outburst rate over the years
following its superoutburst, perhaps resulting from an increased accretion
rate.
