Narrow diameter tubes and especially ͑6,5͒ tubes with a diameter of 0.75 nm are currently one of the most studied carbon nanotubes because their unique optical and especially luminescence response makes them exceptionally suited for biomedical applications. Here we report on a detailed analysis of the electronic structure of nanotubes with ͑6,5͒ and ͑6,4͒ chiralities using a combined experimental and theoretical approach. From high-energy spectroscopy involving x-ray absorption and photoemission spectroscopy the detailed valence-and conduction-band response of these narrow diameter tubes is studied. The observed electronic structure is in sound agreement with state of the art ab initio calculations using density-functional theory.