  We list in increasing order -- 1/3, 3/8, 2/5, 135 pi/1024, 16/(3 pi^2), 3
pi/16, 5/8, 105 pi/512, 2 - 435 pi/1024, 11/16, 1 -- a number of exact
two-qubit Hilbert-Schmidt (HS) separability probabilities, we are able to
compute. Each probability corresponds to a specific scenario -- a class of 4 x
4 density matrices (rho) with an m-subset (m<6) of its six off-diagonal pairs
of symmetrically located entries set to zero. Initially, we consider only
scenarios in which the (6-m) non-nullified pairs are real, but then permit them
to be complex (as well as quaternionic) in nature also. The general analytical
strategy we implement is based on the Bloore density matrix parameterization
(J. Phys. A, 9, 2059 [1976]), allowing us to conveniently reduce the
dimensionalities of required integrations. For each scenario, we identify a
certain univariate ``separability function'' S_{scenario}(nu), where nu =
rho_{11} rho_{44}/(rho_{22} rho_{33}). The integral over nu in [0,infty] of the
product of this function with a scenario-specific (marginal) jacobian function
J_{scenario}(nu) yields the HS {separable} volume (V^{HS}_{sep}). The ratio of
V^{HS}_{sep} to the HS total (entangled and non-entangled) volume, gives us the
HS scenario-specific separability probability. Among the possible forms that we
have so far determined for S_{scenario}(nu) are piecewise combinations of c, c
sqrt{nu} and c nu for nu in [0,1] and (in a dual manner) c, c/sqrt{nu} and c/nu
for nu in [1,infty]. We also obtain bivariate separability functions
S_{scenario)^{6 x 6}(nu_{1},nu_{2}} in the qubit-qutrit case, involving 6 x 6
density matrices, with ratio variables, nu_{1}= rho_{11} rho_{55}/(rho_{22}
rho_{44}), and nu_{2}= rho_{22} rho_{66}/(rho_{33} rho_{55}). Additionally, we
investigate parallel two-qutrit and three-qubit problems.
