Conformal deposition of platinum as ultrathin shells on facet-controlled palladium nanocrystals offers a great opportunity to enhance the catalytic performance while reducing its loading. Here we report such a system based on palladium icosahedra. Owing to lateral confinement imposed by twin boundaries and thus vertical relaxation only, the platinum overlayers evolve into a corrugated structure under compressive strain. For the core-shell nanocrystals with an average of 2.7 platinum overlayers, their specific and platinum mass activities towards oxygen reduction are enhanced by eight- and sevenfold, respectively, relative to a commercial catalyst. Density functional theory calculations indicate that the enhancement can be attributed to the weakened binding of hydroxyl to the compressed platinum surface supported on palladium. After 10,000 testing cycles, the mass activity of the core-shell nanocrystals is still four times higher than the commercial catalyst. These results demonstrate an effective approach to the development of electrocatalysts with greatly enhanced activity and durability.