This paper explores the evolution of the coarsely grained phase-space density in mergers and in galaxy formation. In particular, numerical simulations are used to determine the properties of remnants produced by "major" mergers between equal-mass galaxies. Contrary to some existing claims, remnants of mergers between stellar disks are found to lack sufficient material at high phase-space densities to be identified as elliptical galaxies. We quantify this effect by computing the cumulative coarsely grained phase-space distribution, s(bar∫), for the remnants and compare it to that derived from simple models of the mass profiles of ellipticals. In so doing, we estimate that the discrepancy is confined to the inner ∼15% of the stellar mass. In principle, this problem can be circumvented by dissipation in gas and star formation, but this process by itself probably requires that the progenitors comprise a gas fraction ∼25%-30% of their luminous mass. More directly, as shown by additional simulation, the phase-space discrepancy can be reconciled by including compact bulges in the progenitors having ∼20%-25% the mass of the disks.We further speculate on the relevance of our analyses to more general situations where the progenitor galaxies have very different masses or to remnants produced from repeated mergers in a dense galactic environment. A number of observational signatures are noted which may help to establish the importance of merging to the structure and origin of early-type galaxies. In addition, we apply the methods developed here to the sample of hot stellar systems cataloged recently by Bender et al. A strong correlation is found between the luminosity of these objects and the "effective" coarsely grained phase density (bar∫eff ∝ 1/σr2eff). Implications of these findings for the interpretation of the fundamental plane of elliptical galaxies are discussed.