Medium-amplitude oscillatory shear (MAOS) is asymptotically nonlinear and a valuable tool for inferring structure from rheology. However, a drawback of conventional MAOS is the time and material intensive nature of experiments. Many strain amplitude sweeps, and typically multiple sample loadings, are required to obtain frequency-dependent properties. Here, we propose a new MAOS methodology that is much faster (fewer data points) and cheaper (fewer material loadings): The frequency-sweep MAOS. Similar to conventional frequency-sweep SAOS (small-amplitude oscillatory shear), we use only a frequency-sweep. A key challenge is that measurable MAOS data lie within a narrow and frequency-dependent domain between the instrument resolution (at small strain amplitudes) and nonlinear behavior beyond asymptotic nonlinearity (at large strain amplitudes). This necessitates a nonconstant strain amplitude gamma(0)(omega) for the frequency-sweep instead of a single constant strain amplitude. We provide guidelines for finding this gamma(0)(omega) trajectory for frequency-sweep MAOS. Full characterization of all four MAOS measures requires two frequency-sweeps: One frequency-sweep for the third-harmonic measures and two frequency-sweeps (at different input strain amplitudes) for the first-harmonic measures. We propose criteria to validate this MAOS data taken at a single strain amplitude based on ratios of stress harmonics; a similar idea is extended to validate frequency-sweep SAOS data as well. The proposed method of frequency-sweep MAOS is demonstrated for a polyvinyl alcohol-borax hydrogel. This new, faster, and material economical MAOS approach will be particularly beneficial for precious samples with very limited availability such as model polymers with well-defined architectures. (C) 2017 The Society of Rheology.