I study two-stage hybrid inflation driven by moduli fields, corresponding to flat directions of supersymmetry, lifted by supergravity corrections. The first stage corresponds to a period of either fast-roll or `locked' inflation, induced by an oscillating inflaton. This is followed by a second stage of fast-roll inflation. Enough total e-foldings to encompass the cosmological scales are achieved. Structure in the Universe is generated due to a curvaton field.