Considerable progress has been made towards automatic support for one of the principal techniques available to enhance program reliability: equipping programs with extensive contracts. The results of current contract inference tools are still often unsatisfactory in practice, especially for programmers who already apply some kind of basic Design by Contract discipline, since the inferred contracts tend to be simple assertions - the very ones that programmers find easy to write. We present new, completely automatic inference techniques and a supporting tool, which take advantage of the presence of simple programmer-written contracts in the code to infer sophisticated assertions, involving for example implication and universal quantification.