We show that kinematically peculiar cores may be generated in stellar spiral-spiral mergers. Kinematic segregation appears as the central bulges transport orbital angular momentum inward to the center of the remnant, while the outer parts keep the spin signature of the precursor disks. The peculiar core is composed mostly of bulge material, and its size best matches that of observed peculiar cores for mergers with unequal galaxy masses (~2:1). Population decoupling is predicted by the rapid radial decrease of the bulge fraction in the remnant. In this scenario, a starburst may pump up the remnant metallicity, but otherwise the high metallicity of the kinematically decoupled core is built on the high metal content of the inner bulges rather than on a high self-enrichment of a population built from scratch out of the precursors' gas. Mergers with galaxy mass ratios 3:1 and above generate disk galaxies with counterrotating bulges.