Internal waves are gravity waves that propagate horizontally and vertically within a stratified fluid medium, they are the three-dimensional analogue of surface waves. Internal tides (i.e., internal waves at the tidal frequency) are generated when surface tide currents push stratified fluid up and over sloping bottom topography, causing dramatic vertical displacements of density surfaces in the ocean interior. Here, a non-linear theory is derived for internal-tide generation at tall steep topography. The theory is then compared to a theory for small topography and 160 fully-nonlinear numerical simulations. The new theory agrees well with the numerical simulations and indicates that up to 15% of internal-tide energy end up as 2nd harmonic internal tides. These results indicate why 2nd harmonics are often observed near tall steep topography throughout the global ocean, and they may also help determine the role of tidal dissipation in mixing the ocean.