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Bubbles are ubiquitous in many natural and engineering processes, and bubble bursting aerosols are of particular interest because of their critical role in mass and momentum transfer across interfaces. All prior studies claim that bursting of a millimeter-sized bare bubble at an aqueous surface produces jet drops with a typical size of $\boldsymbol{O}$(100 $\si{\micro\relax}$m), much larger than film drops of $\boldsymbol{O}$(1 $\si{\micro\relax}$m) from the disintegration of a bubble cap. Here, we document the hitherto unknown phenomenon that jet drops can be as small as a few microns when the bursting bubble is coated by a thin oil layer. We provide evidence that the faster and smaller jet drops result from the singular dynamics of the oil-coated cavity collapse. The unique air-oil-water compound interface offers a distinct damping mechanism to smooth out the precursor capillary waves during cavity collapse, leading to a more efficient focusing of the dominant wave and thus allowing singular jets over a much wider parameter space beyond that of a bare bubble. We develop a theoretical explanation for the parameter limits of the singular jet regime by considering the interplay among inertia, surface tension, and viscous effects. As such contaminated bubbles are widely observed, the previously unrecognized fast and small contaminant-laden jet drops may enhance bubble-driven flux across the interface, contributing to the aerosolization and airborne transmission of bulk substances.