Liquid crystal NMR (LX-NMR) spectra of seven different small amides (formamide, acetamide, cis- and trans-N-methylformamide, trans-N-methylacetamide, N,N-dimethylformamide, and N,N-dimethylacetamide) are obtained in the lyotropic liquid crystalline solvent cesium pentadecafluorooctanoate in water (CsPFO/water). Fits of the spectra to a model Hamiltonian yield magnetic dipolar couplings D-ij (where i and j label two nuclear spins). The D-ij are directly related to amide geometry and the details of the orientational distribution of the amide while it visits the bicelle-water interface. Using calculated gas-phase geometries, we extract the orientation tensor S for each amide to within a factor of +/-1. As estimated by the rms magnitude of the eigenvalues of S, the amides vary by a factor of 30 in orientational strength in the following order: trans-N-methylacetamide (S-rms = 0.0031); formamide (0.0038); acetamide (0.010); cis-N-methylformamide (0.011); trans-N-methylformamide (0.066); N,N-dimethylformamide (0.105). N,N-dimethylacetamide orients very strongly, but the spectrum is too complex to analyze. The molecules trans-N-methylformamide and especially N,N-dimethylformamide orient sufficiently strongly to suggest that they must partition to the bicelle-water interface in preference over the bulk water by a factor of 2-3 or more in local concentration. Isomerization about the amide linkage increases orientation strength by a factor of 6 from cis-N-methylformamide to trans-N-methylformamide. The strength of orientation evidently depends primarily on the position of methyl groups. Strong orientation arises in all three molecules with N-methyl, rather than N-H, situated trans to the carbonyl group. Evidently, orientation strength depends only mildly on the total number of methyl groups or on the molecular shape; nor is the electric dipole moment a key factor. A methyl group trans to the carbonyl group allows the carbonyl group to access the hydrogen-bonding environment of the bicelle-water interface, while the methyl group simultaneously inserts in the fluorocarbon core of the CsPFO bicelle. Remarkably, the S tensors for the strong orienters are consistent with such a simple mechanism dominating the angular distribution of the amide within the bicelle-water interface.