I will start reviewing the recent progress in the construction of realistic composite Higgs models, emphasizing the successes and the challenges from flavor physics and precision electro-weak measurements. I will then describe two possible directions to weaken phenomenological bounds. One possibility is to assume that the strong sector from which the Higgs emerges is supersymmetric. Through supersymmetry the dynamical scale of the strong sector could be 10-20 TeV with little fine-tuning, strongly reducing all bounds from compositeness. The soft scalar masses of the light generations are naturally heavy reducing/solving the SUSY flavor problem. In the last part of the talk I will show how the assumption that the Higgs sector is CP symmetric may allow to construct models where all phenomenological bounds are satisfied with a compositeness scale as low as 3 TeV.