  We derive the conditions for a non-equatorial eccentric bound orbit to exist
around a Kerr black hole in two-parameter spaces: the energy, angular momentum
of the test particle, spin of the black hole, and Carter's constant space ($E$,
$L$, $a$, $Q$), and eccentricity, inverse-latus rectum space ($e$, $\mu$, $a$,
$Q$). These conditions distribute various kinds of bound orbits in different
regions of the ($E$, $L$) and ($e$, $\mu$) planes, depending on which pair of
roots of the effective potential forms a bound orbit. We provide a prescription
to select these parameters for bound orbits, which are useful inputs to study
bound trajectory evolution in various astrophysical applications like
simulations of gravitational wave emission from extreme-mass ratio inspirals,
relativistic precession around black holes, and the study of gyroscope
precession as a test of general relativity.
