We study singular jets from the collapse of drop-impact craters, when the drop and pool are of different immiscible liquids. The fastest jets emerge from a dimple at the bottom of the rebounding crater, when no bubble is pinched off. The parameter space is considerably more complex than for identical liquids, revealing intricate compound-dimple shapes. In contrast to the universal capillary–inertial drop pinch-off regime, where the neck radius scales as R ∼ t 2/3, for a purely inertial air dimple the collapse has R ∼ t 1/2. The bottom dimple dynamics is not self-similar but possesses memory effects, being sensitive to initial and boundary conditions. Sequence of capillary waves can therefore mould the air dimple into different collapse shapes, such as bamboo-like and telescopic forms. The finest jets are only 12 μm in diameter and the normalized jetting speeds are up to one order of magnitude larger than for jets from bursting bubbles. We study the cross-over between the two power laws approaching the singularity. The singular jets show the earliest cross-over into the inertial regime. The fastest jets can pinch off a toroidal micro-bubble from the cusp at the base of the jet.