We have developed a systematic design process for recently proposed slanted grating couplers (SGCs) that operates in the strong coupling regime. Based on rigorous analysis of SGC properties, this design process utilizes the k-vector diagram and a rigorous grating leaky-mode solver to intentionally enforce the phase-match and Bragg conditions. We demonstrate that the resultant SGC designs have performance similar to those obtained by parallel micro-genetic algorithm (µGA) optimization with the twodimensional finite-difference time-domain (2D FDTD) method. Only two 2D FDTD simulations are necessary in the later stages of our systematic design process. Therefore the time saving is tremendous compared to a µGA 2D FDTD design tool, which can require thousands of individual 2D FDTD simulation runs. We illustrate the utility of our new systematic design process with an embedded slanted grating coupler example.