An axially symmetric inviscid shallow-water model (SWM) on the rotating Earth forced by off-equatorial steady differential heating is employed to characterize the main features of the upper branch of an ideal Hadley circulation. The steady-state solutions are derived and analyzed and their relevance to asymptotic temporal evolution of the circulation is established by comparing them to numerically derived timedependent solutions at long times. The main novel feature of the steady-state solutions of the present theory is the existence of a tropical region, associated with the rising branch of the Hadley circulation, which extends to about half the combined width of the Hadley cells in the two hemispheres and is dominated by strong vertical advection of momentum. The solutions in this tropical region are characterized by three conditions: (i) the meridional temperature gradient is very weak but drastically increases outside of the region, (ii) moderate easterlies exist only inside this region and they peak off the equator, and (iii) angular momentum is not conserved there. The momentum fluxes of the new solutions at the tropics differ qualitatively from those of existing nearly inviscid theories and the new flux estimates are in better agreement with both observations and axially symmetric simulations. As in previous nearly inviscid theories, the steady solutions of the new theory are determined by a thermal Rossby number and by the latitude of maximal heating.