ITIL needs more from outside in order to fully support IT governance.
For the quality aspect Six Sigma is a strong contender. Since General Electric announced huge savings this “critical to quality” approach has become popular (an article around cost reduction for several well known companies is here).
Six Sigma is a methodology that systematically improves processes by eliminating defects. The goal is to achieve exceptional quality among the competition by reducing effects to 3.4 defects (or less) per one million opportunities.