Accurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and post-W4 theories. For a set of 28 first- and second-row diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords near-spectroscopic or better predictions. Specifically, the root-mean-square deviations (RMSDs) from experiment are 0.04 pm for the equilibrium bond distances (re ), 1.03 cm −1 1.03 cm−1 for the harmonic frequencies (ωe) , 0.20 cm −1 0.20 cm−1 for the first anharmonicity constants (ωexe) , 0.10 cm −1 0.10 cm−1 for the second anharmonicity constants (ωeye) , and 0.001 cm −1 0.001 cm−1 for the vibration-rotation coupling constants (α e ) . These RMSDs imply 95% confidence intervals of about 0.1 pm for r e , 2.0 cm −1 2.0 cm−1 for ω e ωe , 0.4 cm −1 0.4 cm−1 for ωexe, and 0.2 cm −1 0.2 cm−1 for ωe ye. We find that post-CCSD(T) contributions are essential to achieve such narrow confidence intervals for r e re and ω e ωe , but have little effect on ω e x e ωexe and α e αe , and virtually none on ω e y e ωeye . Higher-order connected triples T ˆ 3 −(T) T̂3−(T) improve the agreement with experiment for the hydride systems, but their inclusion (in the absence of T ˆ 4 T̂4 ) tends to worsen the agreement with experiment for the nonhydride systems. Connected quadruple excitations T ˆ 4 T̂4 have significant and systematic effects on r e , ωe , and ωe xe , in particular they universally increase re (by up to 0.5 pm), universally reduce ωe (by up to 32 cm −1 32 cm−1 ), and universally increase ωex e (by up to 1 cm −1 1 cm−1 ). Connected quintuple excitations T ˆ 5 T̂5 are spectroscopically significant for ω e ωe of the nonhydride systems, affecting ωe by up to 4 cm −1 4 cm−1 . Diagonal Born–Oppenheimer corrections have systematic and spectroscopically significant effects on re and ωe of the hydride systems, universally increasing r e re by 0.01–0.06 pm and decreasing ω e ωe by 0.3–2.1 cm −1 0.3–2.1 cm−1 . Obtaining r e re and ω e ωe of the pathologically multireference BN and BeO systems with near-spectroscopic accuracy requires large basis sets in the core-valence CCSD(T) step and augmented basis sets in the valence post-CCSD(T) steps in W4 theory. The triatomic molecules H2 O , CO2 , and O3 are also considered. The equilibrium geometries and harmonic frequencies (with the exception of the asymmetric stretch of O3 ) are obtained with near-spectroscopic accuracy at the W4 level. The asymmetric stretch of ozone represents a severe challenge to W4 theory, in particular the connected quadruple contribution converges very slowly with the basis set size. Finally, the importance of post-CCSD(T) correlation effects for electrical properties, namely, dipole moments(μ), polarizabilities (α) , and first hyperpolarizabilities (β), is evaluated.