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This paper compares two alternative characterizations of chaotic orbit segments, one based on the complexity of their Fourier spectra, as probed by the number of frequencies n(k) required to capture a fixed fraction k of the total power, and the other based on the computed values of short-time Lyapunov exponents chi. An analysis of orbit ensembles evolved in several different two- and three-dimensional potentials reveals that there is a strong, roughly linear correlation between these alternative characterizations, and that computed distributions of complexities, N[n(k)] and short-time chi, N[chi] often assume similar shapes. This corroborates the intuition that chaotic segments which are especially unstable should have Fourier spectra with particularly broad-band power. It follows that orbital complexities can be used as probes of phase space transport and other related phenomena in the same manner as can short-time Lyapunov exponents.