We present the properties and advantages of a new magneto-optical trap (MOT) where blue- detuned light drives ‘type-II’ transitions that have dark ground states. Using ⁸⁷Rb, we reach a radiation-pressure-limited density exceeding 10¹¹ cm⁻³ and a temperature below 30 μK. The phase-space density is higher than in normal atomic MOTs, and a million times higher than comparable red-detuned type-II MOTs, making the blue-detuned MOT particularly attractive for molecular MOTs which rely on type-II transitions. The loss of atoms from the trap is dominated by ultracold collisions between Rb atoms. For typical trapping conditions, we measure a loss rate of 1.8(4) × 10⁻¹⁰ cm³ s⁻¹.