Re-examination of the properties of distant galaxies leads to evidence that most present-day spirals built up half of their stellar masses during the last 8 Gyr, mostly during several intense phases of star formation during which they resembled luminous infrared galaxies (LIRGs). Distant galaxy morphologies encompass all of the expected stages of galaxy merging, central core formation and disk growth, while their cores are much bluer than those of present-day bulges. We have tested a spiral rebuilding scenario, in which 75 ± 25% of spirals experienced their last major merger event less than 8 Gyr ago. It accounts for the simultaneous decreases, during that period, of the cosmic star-formation density, of the merger rate, of the number densities of LIRGs and of compact galaxies, while the densities of ellipticals and large spirals are essentially unaffected.