Semicrystalline polymers such as polyethylene or polypropylene combine stiffness and toughness due to alternating rigid nanocrystallites and soft amorphous layers. As a result of chain connectivity across the crystalline-amorphous interface, the traditional structural models unintentionally but unavoidably produce excess density in the noncrystalline reqions. We have identified the avoidance of such density anomalies as a guiding principle for predicting structural features such as chain ends at the crystal surface or pronounced chain tilt in the crystallites that reduce the chain crowding at the interface. We are using NMR and other techniques to document these predictions.