A new method to design punctured Turbo Codes (TCs) with improved performance in both the waterfall and error floor regions is introduced. First, the puncturing pattern is selected by analyzing the constituent code distance spectrum and the TC extrinsic information exchange using uniform interleavers. Then, the interleaver function is defined via a graph-based approach including different design criteria such as minimum span, correlation girth, and puncturing constraints during the design process. An application example is elaborated and compared with the Long Term Evolution (LTE) standard: a significant gain in error rate performance can be observed. An additional benefit of the proposed technique is a significant reduction of the search space for the different interleaver parameters.