We designed a grating coupler optimized for normal incidence and numerically demonstrate near-unity coupling in a standard 220-nm-thick silicon-on-insulator (SOI) technology. Our design breaks the vertical symmetry within the grating region by implementing three scattering sites per local period. This technique removes the need for bottom reflectors or additional material layers and can be realized using only two lithography masks. Using adjoint method-based optimization, we engineer the coupling spectrum of the grating, balancing the trade-off between peak efficiency and bandwidth. Using this technique, we simulate three devices with peak coupling efficiencies ranging between 93.4 (-0.3 dB) and 98.6% (-0.06 dB) with corresponding 1 dB bandwidths between 48 and 8 nm all centered around 1.55 µm.