The dynamics of the merger between a high- and a low-luminosity elliptical galaxy has been studied to understand how kinematically peculiar cores in elliptical galaxies might form. Numerical simulations of mergers provide rotation curves, surface density profiles, surface density contour plots and velocity maps of the merger remnants, as well as diagnostics on the dynamics such as phase-space diagrams. This type of merger can create counterrotating cores. The core of the smaller galaxy, of higher density, is not disrupted by the primary tidal field and sinks to the center of the primary as an independent dynamical subsystem. Core counterrotation occurs only when the initial merger orbit is retrograde with respect to the spin of the primary. The remnant has higher effective radius and lower mean central surface density than the primary galaxy, but a smaller core radius. The adsorption of orbital energy and angular momentum by the primary particles greatly modifies the kinematic structure of the larger galaxy. Twisted rotation axes and isophote twists appear over the whole body of the remnant. These diagnostics may be used to determine whether observed peculiar cores might have formed via an elliptical-elliptical merger. Galaxies with counterrotating cores should show a complex velocity field, isophotal irregularities, and, in general, a slow rotation in the main body of the galaxy. The present experiments are the first galaxy-satellite merger experiments involving an active, rotating secondary. They show that part of the orbital angular momentum is absorbed by the secondary, thus the secondary contributes to its own sinking: the sinking rate depends on the orientation of the secondary spin. Long-slit spectroscopic observations of NGC 3656 are reported. Rotation curves indicate that NGC 3656 contains a core spinning in a direction perpendicular to the rotation in the main body of the galaxy. Velocity reversals at intermediate radii are also observed. These features are interpreted as the signature of a recent merger. It is unlikely that the counterrotating core has formed from the gas in the conspicuous dust band that runs across the galaxy because their respective angular momenta are perpendicular. NGC 3656 appears to be the site of a multi-merger event.