Detailed simulations of the Compact Ignition Tokamak are carried out using a 1½-dimensional transport code. The calculations include time-varying densities, fields, and plasma shape. Ignition can be achieved in this device if somewhat better than L-mode energy confinement time scaling is possible. The performance of such a compact, short-pulse device can depend greatly on how the plasma is evolved to its flattop parameters. Furthermore, in cases such as the ones discussed here, where there is not a great deal of ignition margin and the electron density is held constant, ignition ends if the helium ash is not removed. In general, control of the deuterium-tritium density is equivalent to burn control.