For proofs by induction it is often necessary to generalize statements to strengthen the induction hypotheses.  We present improved heuristics to generalize away subterms, unnecessary conditions and function symbols in a formula.  This resolves shortcomings that we encountered within an experimental evaluation of generalization heuristics from the literature.  Our
generalization method has been implemented in the verification tool VeriFun. An
evaluation with examples from the literature as well as several case studies of our own demonstrates the success of our development.