  The micro-canonical phase-space volume for the three-body problem is an
elementary quantity of intrinsic interest, and within the flux-based
statistical theory, it sets the scale of the disintegration time. While the
bare phase-volume diverges, we show that a regularized version can be defined
by subtracting a reference phase-volume, which is associated with hierarchical
configurations. The reference quantity, also known as a counter-term, can be
chosen from a 1-parameter class. The regularized phase-volume of a given
(negative) total energy, $\bar\sigma(E)$, is evaluated. First, it is reduced to
a function of the masses only, which is sensitive to the choice of a
regularization scheme only through an additive constant. Then, analytic
integration is used to reduce the integration to a sphere, known as shape
sphere. Finally, the remaining integral is evaluated numerically, and presented
by a contour plot in parameter space. Regularized phase-volumes are presented
for both the planar three-body system and the full 3d system. In the test mass
limit, the regularized phase-volume is found to become negative, thereby
signalling the breakdown of the non-hierarchical statistical theory. This work
opens the road to the evaluation of $\bar\sigma(E,L)$, where $L$ is the total
angular momentum, and it turn, to comparison with simulation determined
disintegration times.
