  It is well-known that the light curve of a transiting planet contains
information about the planet's orbital period and size relative to the host
star. More recently, it has been demonstrated that a tight constraint on an
individual planet's eccentricity can sometimes be derived from the light curve
via the "photoeccentric effect," the effect of a planet's eccentricity on the
shape and duration of its light curve. This has only been studied for large
planets and high signal-to-noise scenarios, raising the question of how well it
can be measured for smaller planets or low signal-to-noise cases. We explore
the limits of the photoeccentric effect over a wide range of planet parameters.
The method hinges upon measuring $g$ directly from the light curve, where $g$
is the ratio of the planet's speed (projected on the plane of the sky) during
transit to the speed expected for a circular orbit. We find that when the
signal-to-noise in the measurement of $g$ is $< 10$, the ability to measure
eccentricity with the photoeccentric effect decreases. We develop a "rule of
thumb" that for per-point relative photometric uncertainties $\sigma = \{
10^{-3}, 10^{-4}, 10^{-5} \}$, the critical values of planet-star radius ratio
are $R_p / R_\star \approx \{ 0.1, 0.05, 0.03 \}$ for Kepler-like 30-minute
integration times. We demonstrate how to predict the best-case uncertainty in
eccentricity that can be found with the photoeccentric effect for any light
curve. This clears the path to study eccentricities of individual planets of
various sizes in the Kepler sample and future transit surveys.
