Beside the classic Fe${}_{64}$Ni${}_{36}$ Invar alloy, which shows an anomalously low thermal expansion at ambient pressure, Fe-Ni alloys with a higher nickel composition can be driven to Invar behavior by pressure. The authors investigate the pressure induced Invar effect theoretically and demonstrate that it can be explained by a magnetic transition from a ferromagnetic state at high volume to a complex noncollinear state upon compression. They relate the Invar effect to the increasing contribution of magnetic entropy with pressure.