Studies on the break-up of a liquid drop or an air bubble reveal that the dynamics prior to a singularity can have several forms, ranging from universal, with no memory of the initial state, or integrable, which has a complete memory. We find that how an air bubble disconnects from an underwater nozzle is associated with an unusually rich class of dynamics, one reflecting the integrable singularity of the cylindrically symmetric break-up. Dynamics that are weakly distorted from cylindrical symmetry support vibrations whose amplitudes freeze as disconnection approaches, thus encoding details about the initial distortion. As a result, even a slight asymmetry entirely changes the nature of the singularity. Instead of collapsing down to a point, the bubble neck evolves towards a double column shape.