The conformations and motions of lipid molecules under different membrane curvatures have important implications for transmembrane protein function, binding events, and overall membrane organization. This work reports on the local order parameters of saturated lipid molecules, as measured by C-13 NMR relaxation, under several curvature conditions to probe structural changes as a function of lipid bilayer curvature. Different curvature conditions are created by depositing phosphatidylcholine membranes on spherical beads of various diameters. The findings reveal that the order parameters are not a continuous function of the membrane curvature. While small (30 nm) and large (110 nm) diameter bilayers exhibit similar order parameters, bilayers with curvatures of 60-80 nm diameter show a consistently increased order parameter along the entire lipid molecule, indicating a higher packing density and lateral tension. Order parameters for curvatures between 60 and 80 nm also show molecular evidence for interdigitation.