A series of isotropic compression tests and drained and undrained triaxial compression tests have been performed on glacial sediment from Iceland. Langjökull sediment, which is well graded, is thought to have reached a critical grading during deposition and transportation. Multiple parallel normal compression lines (NCLs) were found, but a unique critical state line (CSL) could be identified. This is unlike other so-called “transitional” soils, whose grading varies between reasonably well graded to gap graded, which tend to have distinct NCLs and critical state lines depending on the specimen density. It is thought that in the case of the Langjökull sediment studied, its particular strain history that involved incessant shearing during deposition accounts for the difference in behaviour. This provides the interesting case of a soil that has been crushed to a critical grading in situ, which depends on the mineralogy of the grains, which was then sampled and tested. Despite the unique grading, samples with a range of different void ratios can be prepared and the combination of grading and density seems to set a fabric that cannot be changed by compression, resulting in multiple parallel NCLs. At the critical state, however, the fabric has been destroyed and the CSL is unique.