Although galaxies, groups, and clusters contain ∼10% of the baryons, many more reside in the photoionized and shocked-heated intergalactic medium (IGM) and in the circumgalactic medium (CGM). We update the baryon census in the (H i) Lyα forest and warm-hot IGM (WHIM) at 105–6 K traced by O vi λ1032, 1038 absorption. From Enzo cosmological simulations of heating, cooling, and metal transport, we improve the H i and O vi baryon surveys using spatially averaged corrections for metallicity (Z/Z☉) and ionization fractions (fH i, fO vi). Statistically, the O vi correction product correlates with column density, (Z/Z☉)fO vi ≈ (0.015)(NO vi/1014 cm−2)0.70, with an NO vi-weighted mean of 0.01, which doubles previous estimates of WHIM baryon content. We also update the Lyα forest contribution to baryon density out to z = 0.4, correcting for the (1 + z)3 increase in absorber density, the (1 + z)4.4 rise in photoionizing background, and cosmological proper length dℓ/dz. We find substantial baryon fractions in the photoionized Lyα forest (28% ± 11%) and WHIM traced by O vi and broad-Lyα absorbers (25% ± 8%). The collapsed phase (galaxies, groups, clusters, CGM) contains 18% ± 4%, leaving an apparent baryon shortfall of 29% ± 13%. Our simulations suggest that ∼15% reside in hotter WHIM (T ⩾ 106 K). Additional baryons could be detected in weaker Lyα and O vi absorbers. Further progress requires higher-precision baryon surveys of weak absorbers, down to minimum column densities NH i ⩾ 1012.0 cm−2, NO vi ⩾ 1012.5 cm−2, NO vii ⩾ 1014.5 cm−2, using high signal-to-noise data from high-resolution UV and X-ray spectrographs.