We present a framework for obtaining high quality relaxed graded SiGe buffers on Si for III-V integration. By avoiding dislocation nucleation in Si1−xGex layers of x>0.96, we have achieved a relaxed Si0.04Ge0.96 platform on Si(001) offcut 2° that has a threading dislocation density of 7.4×105 cm−2. This 2° offcut orientation was determined to be the minimum necessary for APB-free growth of GaAs. Furthermore, we found that we could compositionally grade the Ge content in the high-Ge portion of the buffer at up to 17 %Ge μm−1 with no penalty to the dislocation density. The reduction in both threading dislocation density and buffer thickness exhibited by our method is an especially significant development for relatively thick minority-carrier devices which use III-V materials such as multi-junction solar cells.