Statistical results are presented from Polar/CAMMICE measurements of events during which the plasma sheet ions have penetrated deeply into the inner magnetosphere. Owing to their characteristic structure in energy-time spectrograms, these events are called "intense nose events." Almost 400 observations of such structures were made during 1997. Intense nose events are shown to be more frequent in the dusk than in the dawn sector. They typically penetrate well inside L = 4, the deepest penetration having occurred around midnight and noon. The intense nose events are associated with magnetic (substorm) activity. However, even moderate activity (AE = 150-250 nT) resulted in formation of these structures. In a case study of November 3, 1997, three sequential inner magnetosphere crossings of the Polar and Interball Auroral spacecraft are shown, each of which exhibited signatures of intense nose-like structures. Using the innermost boundary determinations from these observations, it is demonstrated that a large-scale convective electric field alone cannot account for the inward motion of the structure. It is suggested that the intense nose structures are caused by short-lived intense electric fields (in excess of ∼1 mV/m) in the inner tail at L=4-5.