Details of simultaneous photometric and spectroscopic observations of
the optical counterpart of the ''supersoft'' X-ray source in the Small
Magellanic Cloud, 1E 0035.4-7230 (SMC 13), are presented. Although th
e spectrum is dominated by emission lines of He II, the Balmer series
of hydrogen is also present in emission with a strong decrement, and B
almer lines are seen as broad absorptions. Several high-ionization emi
ssion features are also present, including O VI (at 3811, 3834, and 52
90 Angstrom). Radial velocities and photometry confirm that the binary
period is similar to 0(d).1719, and an improved value of the period i
s derived from 4 years of photometry and analysis of ROSAT HRI X-ray d
ata. The orbital light variation is primarily due to an eclipse of the
extensive accretion disk. X-ray and optical minima occur together. Th
e UBV light curves are similar to each other, and no clear phase-relat
ed color variations are found. He II emission-line velocities show a s
emiamplitude of K similar to 100 km s(-1), and maximum velocity occurs
when the light curve indicates that the compact star would be moving
away from the observer, suggesting that this emitting region may trace
the orbital motion of the compact star. The range of possible masses
implied for the X-ray source lies between 0.5 and 1.5 M-. if the mass
donor is a main-sequence star filling its Roche lobe. The light curve
suggests values at the high end of this range. The broad H absorption
lines appear to have a much larger velocity amplitude and a lower syst
emic velocity, making it difficult to understand their origin. We disc
uss possible models for the system.