6% is about the best we can do with a closed cycle. Extra-terrestrial sources could push those numbers even lower by running up to a pure D-He3 reaction.
If we get really good at fusion we could also use boron fusion. It uses the most common isotope of boron, which is plentiful on Earth, plus regular hydrogen, and the main reaction is aneutronic. There'd be some minor side reactions but it'd be under 1% of energy as neutron radiation, probably better than you'd get with deuterium in the mix.