  The importance of post-CCSD(T) corrections as high as CCSDTQ56 for
ground-state spectroscopic constants ($D_e$, $\omega_e$, $\omega_ex_e$, and
$\alpha_e$) has been surveyed for a sample of two dozen mostly heavy-atom
diatomics spanning a broad range of static correlation strength. While CCSD(T)
is known to be an unusually felicitous `Pauling point' between accuracy and
computational cost, performance leaves something to be desired for molecules
with strong static correlation. We find CCSDT(Q)$_\Lambda$ to be the next
`sweet spot' up, of comparable or superior quality to the much more expensive
CCSDTQ. A similar comparison applies to CCSDTQ(5)$_\Lambda$ vs. CCSDTQ5, while
CCSDTQ5(6)$_\Lambda$ is essentially indistinguishable from CCSDTQ56. A
composite of CCSD(T)-X2C/ACV5Z-X2C with [CCSDT(Q)$_\Lambda$ -- CCSD(T)]/cc-pVTZ
or even cc-pVDZ basis sets appears highly effective for computational
vibrational spectroscopy. Unlike CCSDT(Q) which breaks down for the ozone
vibrational frequencies, CCSDT(Q)$_\Lambda$ handles them gracefully.
