The rotational spectrum of N-acetyl alanine methyl ester, a derivative of the biomimetic, N-acetyl alanine N'-methyl amide or alanine dipeptide, has been measured using a mini Fourier transform spectrometer between 9 and 25 GHz as part of a project undertaken to determine the conformational structures of various peptide mimetics from the torsion-rotation parameters of low-barrier methyl tops. Torsion-rotation splittings from two of the three methyl tops capping the acetyl end of the -NH-C(=O)- and the methoxy end of -C(=O)-O- groups account for most of the observed lines. In addition to the AA state, two E states have been assigned and include an AE state having a torsional barrier of 396.45(7) cm(-1) (methoxy rotor) and an EA state having a barrier of 64.96(4) cm(-1) (acetyl rotor). The observed torsional barriers and rotational constants of alanine dipeptide and its methyl ester are compared with predictions from Möller-Plesset second-order perturbation theory (MP2) and density functional theory (DFT) in an effort to explore systematic errors at the two levels of theory. After accounting for zero-point energy differences, the torsional barriers at the MP2/cc-pVTZ level are in excellent agreement with experiment for the acetyl and methoxy groups while DFT predictions range from 8% to 80% too high or low. DFT is found to consistently overestimate the overall molecular size while MP2 methods give structures that are undersized. Structural discrepancies of similar magnitude are evident in previous DFT results of crystalline peptides.