  Eisenbud and Harris introduced the theory of limit linear series, and
constructed a space parametrizing their limit linear series. Recently, Osserman
introduced a new space which compactifies the Eisenbud-Harris construction. In
the Eisenbud-Harris space, the set of refined limit linear series is always
dense on a general reducible curve. Osserman asks when the same is true for his
space. In this paper, we answer his question by characterizing the situations
when the crude limit linear series contain an open subset of his space.
