Ionization-induced injection into a laser-driven wakefield is studied using 2½D OSIRIS simulations. A laser propagates into a gas mixture of 99.5% helium and 0.5% nitrogen with gas density of each rising linearly from 0 to a peak, after which these remain constant. Simulations show that the process can be controlled by varying the scale length of an up-ramp, the laser intensity, and the maximum plasma density. The injection process is controlled by the bubble radius decreasing as laser propagates up the density gradient and laser self-focusing in the flat-top region. A beam with a central energy of 350 MeV and an energy spread (FWHM) of 1.62% was obtained for an up-ramp length of 135 μm, a normalized vector potential of 2, and a density of 7 × 1018cm−3 (assuming a 0.8 μm wavelength laser).