  We consider the question "Is every nonzero generic degree a
density-1-bounding generic degree?" By previous results \cite{I2} either
resolution of this question would answer an open question concerning the
structure of the generic degrees: A positive result would prove that there are
no minimal generic degrees, and a negative result would prove that there exist
minimal pairs in the generic degrees.
  We consider several techniques for showing that the answer might be positive,
and use those techniques to prove that a wide class of assumptions is
sufficient to prove density-1-bounding.
  We also consider a historic difficulty in constructing a potential
counterexample: By previous results \cite{I1} any generic degree that is not
density-1-bounding must be quasiminimal, so in particular, any construction of
a non-density-1-bounding generic degree must use a method that is able to
construct a quasiminimal generic degree. However, all previously known examples
of quasiminimal sets are also density-1, and so trivially density-1-bounding.
We provide several examples of non-density-1 sets that are quasiminimal.
  Using cofinite and mod-finite reducibility, we extend our results to the
uniform coarse degrees, and to the nonuniform generic degrees. We define all of
the above terms, and we provide independent motivation for the study of each of
them.
  Combined with a concurrently written paper of Hirschfeldt, Jockusch, Kuyper,
and Schupp \cite{HJKS}, this paper provides a characterization of the level of
randomness required to ensure quasiminimality in the uniform and nonuniform
coarse and generic degrees.
