  One proposed method for finding terrestrial planets around nearby stars is to
use two spacecraft--a telescope and a specially shaped occulter that is
specifically designed to prevent all but a tiny fraction of the starlight from
diffracting into the telescope. As the cost and observing cadence for such a
mission will be driven largely by the separation between the two spacecraft, it
is critically important to design an occulter that can meet the observing goals
while flying as close to the telescope as possible. In this paper, we explore
this tradeoff between separation and occulter diameter. More specifically, we
present a method for designing the shape of the outer edge of an occulter that
is as small as possible and gives a shadow that is deep enough and large enough
for a 4m telescope to survey the habitable zones of many stars for Earth-like
planets. In particular, we show that in order for a 4m telescope to detect in
broadband visible light a planet 0.06 arcseconds from a star shining $10^{10}$
times brighter than the planet requires a specially-shaped occulter 50m in
diameter positioned about $72,000$ km in front of the telescope.
