We use newly observed and published near-infrared spectra, together with synthetic spectra obtained from model atmospheres, to derive physical properties of three of the latest type T dwarfs. A new R ≈ 1700 spectrum of the T7.5 dwarf HD 3651B, together with existing data, allows a detailed comparison to the well-studied and very similar dwarf Gl 570D. We find that HD 3651B has both higher gravity and higher metallicity than Gl 570D, with best-fit atmospheric parameters of T_eff = 820-830 K, log g = 5.4-5.5, [m/H] = +0.2, and K_zz = 10⁴ cm² s^-1. Its age is 8-12 Gyr, and its implied mass is 60-70 M_J. We perform a similar analysis of the T8 and T7.5 dwarfs 2MASS J09393548-2448279 and 2MASS J11145133-2618235 using published data, comparing them to the well-studied T8, 2MASS J04151954-0935066. We find that these two dwarfs have effectively the same T_eff as the reference dwarf, and similar or slightly higher gravities, but lower metallicities. The derived parameters are T_eff = 725-775 K and [m/H] = -0.3; log g = 5.3 - 5.45 for 2MASS J09393548-2448279 and log g = 5.0 - 5.3 for 2MASS J11145133-261823. The age and mass are ~10 Gyr and 60 M_J for 2MASS J09393548-2448279, and ~5 Gyr and 40 M_J for 2MASS J11145133-261823. A serious limitation to such analyses is the incompleteness of the line lists for transitions of CH₄ and NH₃ at λ ≤ 1.7 μm, which are also needed for synthesizing the spectrum of the later, cooler, Y type. Spectra of Saturn and Jupiter, and of laboratory CH₄ and NH₃ gas, suggest that NH₃ features in the Y and J bands may be useful as indicators of the next spectral type, and not features in the H and K bands, as previously thought. However, until cooler objects are found, or the line lists improve, large uncertainties remain, as the abundance of NH₃ is likely to be significantly below the chemical equilibrium value. Moreover, inclusion of laboratory NH₃ opacities in our models predicts band shapes that are discrepant with existing data. It is possible that the T spectral class will have to be extended to temperatures around 400 K, when water clouds condense in the atmosphere and dramatically change the spectral energy distribution of the brown dwarf.