We report strong repeated magnetic reconnection pulses that occurred deep inside closed plasma sheet flux tubes at r ≤ 14Re. They have been observed with a fortuitous spacecraft constellation during three consecutive turbulent magnetic dipolarizations, accompanied by localized auroral brightenings near the equatorward edge of a wide auroral oval. The reconnection separatrix was mapped to ~64¿ CGLat in the ionosphere, where a very energetic and narrow energy-dispersed ion injection with unusually steep dispersion slope was observed. Reconstruction of the reconnection rate from magnetic waveforms at Cluster provided a reconnection pulse duration (~1 min) and peak strength (E R ~ 8 mV/m) consistent with direct observations in the reconnection outflow region. The magnetic activity was rather weak, although the concurrent solar wind flow pressure was above the norm. We suggest that near-Earth reconnection events may be a phenomenon more frequent than generally thought. We also confirm that reconnection and the growth of strong turbulence in the near tail are strongly coupled together in near-Earth reconnection events.