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) Lyalpha forest and warm-hot IGM (WHIM) at 10 super(5-6) K traced by O VI lambda1032, 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 sub(middot in circle)) and ionization fractions (f sub(H I), f sub(O VI)). Statistically, the O VI correction product correlates with column density, (Z/Z sub(middot in circle))f sub(O VI) approximately (0.015)(N sub(O VI)/10 super(14) cm super(-2)) super(0.70), with an N sub(O VI)-weighted mean of 0.01, which doubles previous estimates of WHIM baryon content. We also update the Lyalpha forest contribution to baryon density out to z = 0.4, correcting for the (1 + z) super(3) increase in absorber density, the (1 + z) super(4.4) rise in photoionizing background, and cosmological proper length dl/dz. We find substantial baryon fractions in the photoionized Lyalpha forest (28% + or - 11%) and WHIM traced by O VI and broad-Lyalpha absorbers (25% + or - 8%). The collapsed phase (galaxies, groups, clusters, CGM) contains 18% + or - 4%, leaving an apparent baryon shortfall of 29% + or - 13%. Our simulations suggest that ~15% reside in hotter WHIM (T > or =, slanted 10 super(6) K). Additional baryons could be detected in weaker Lyalpha and O VI absorbers. Further progress requires higher-precision baryon surveys of weak absorbers, down to minimum column densities N sub(H I) > or =, slanted 10 super(12.0) cm super(-2), N sub(O VI) > or =, slanted 10 super(12.5) cm super(-2), N sub(O VII) > or =, slanted 10 super(14.5) cm super(-2), using high signal-to-noise data from high-resolution UV and X-ray spectrographs.