We request 13.9 hours of IRS GTO time to observe two recently discovered very low-mass T dwarfs, the early-T HN PegB and the very late-T ULAS J0034. As inferred from models, the two T dwarfs have similar masses of around 20 MJupiter, and similar gravities, but very different effective temperatures of Teff ~1100 K and 650 K for HN PegB and ULAS J0034, respectively. The warmer T dwarf is of special interest as models currently cannot reproduce the flux distributions of the early-T dwarfs. HN PegB is the only early-T dwarf that is observable with the IRS that is also a companion to a main sequence star, so that age and metallicity can be constrained. The cooler T dwarf is of special interest as it is the coolest T dwarf currently known. The IRS data will allow us to complete the spectral energy distributions of these key brown dwarfs, for which near-infrared and IRAC data are already available. This will in turn enable a better determination of the fundamental parameters Teff, gravity and metallicity, as well as allow a study of the clearing of the cloud decks in the early-T dwarf, and of the chemical mixing due to vertical transport in the atmosphere of the late-T dwarf. Constraining these parameters and processes will allow refinement of the mass and age determinations for these important dwarfs.