We discuss constraints from perturbative unitarity and crossing on the leading contributions of the higher-dimension operators to the four-graviton amplitude in four spacetime dimensions. We focus on the leading order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest IR finite. To test the constraints we obtain nontrivial effective field theory data by computing and taking the large mass expansion of the one-loop minimally coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, the leading EFT corrections to Einstein gravity of physical theories, both string theory and QFT coupled to gravity, end up in minuscule islands which are much smaller than what is suggested by the generic bounds obtained from consistency of the 2-2 graviton scattering amplitude. We discuss the underlying mechanism for this phenomenon.