  The uniquess of the effective actions describing 4D SU(2) and SU(3)
continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and
preconfining phases is made explicit. Subsequently, the spatial string tension
is computed in the approach proposed by Korthals-Altes. This SU(2) calculation
is based on a particular, effective two-loop correction to the pressure needed
for the extraction of the hypothetic number density of isolated and screened
magnetic monopoles or antimonopoles in the deconfining phase. By exponentiating
the exchange of the tree-level massless but one-loop dressed mode within a
quadratic spatial contour of side-length $L$ in the effective theory we
demonstrate that for $L\to\infty$ the Wilson loop exhibits {\sl perimeter} law.
This is in contrast to a rigorous {\sl lattice} result subject to the Wilson
action and for this action valid at sufficiently high temperature. In the
framework of the effective theory there is, however, a regime for small
(spatially unresolved) $L$ were the exponent of the spatial Wilson loop
possesses curvature as a function of $L$.
