  We scrutinize, improve some determinations of the masses and couplings of
light scalar quarkonia ($\bar qq$ and four-quark states) and present new
results for the $\pi^+\pi^-,K^+K^-,\dots$ molecules using QCD Laplace Sum Rule
(LSR) truncated at the $D=6$ dimension vacuum condensates. We pay a special
attention on the higher order perturbative (PT) corrections up to the
(estimated) ${\cal O}(\alpha_s^5)$ which improve the quality of the analysis.
We request that the optimal results obey the rigorous constraint: {\it
Resonance $\geq$ QCD continuum contributions ($R_{P/C}\geq 1$)} in the LSR
which excludes a Breit-Wigner / on-shell (not to be confused with a complex
pole) scalar meson mass around (500-600) MeV obtained for values [$t_c\leq
(1\sim 1.5)$ GeV$^2$] of the QCD continuum threshold. Mass-splittings due to
$SU3$ breakings are small. We discuss the different assignements of the
observed scalar mesons below 2 GeV in the Conclusions where the $I=0$ states
are compared with the scalar gluonia. The results are compiled in Table 3 to 6.
