Strongly peaked electron density profiles have been obtained in ASDEX by different refuelling methods: pellet fuelling (ohmic and co-injection heating), NBI counter-injection and recently by reduced gas puff fuelling scenarios. These discharges show in common increased density limits, a canonical electron temperature profile independent of the density profile and an improvement of the particle and energy confinement. Whereas the changes in particle transport are not fully understood, transport analyses point out that the improved energy transport can be explained by reduced ion conduction losses coming close to the neoclassical ones. The different results for the ion transport with flat and peaked density profiles are quantitatively consistent with that expected from eta i-driven modes. The analyses cannot yet explain the anomalous electron energy transport, apart from identified continuous trends such as inverse scaling with the isotope mass and enhancement with heating power.