  The mu-invariant mu = (\mu_1,\mu_2,\mu_3) of a rational space curve gives
important information about the curve. In this paper, we describe the structure
of all parameterizations that have the same mu-type, what we call a mu-stratum,
and as well the closure of strata. Many of our results are based on papers by
the second author that appeared in the commutative algebra literature. We also
present new results not in the earlier papers, including an explicit formula
for the codimension of the locus of non-proper parametrizations within each
mu-stratum and a decomposition of the smallest mu-stratum based on which
two-dimensional rational normal scroll the curve lies on.
