Local measurements of the Hubble parameter are increasingly in tension with the value inferred from a $Lambda$CDM fit to the cosmic microwave background (CMB) data. In this paper, we construct scenarios in which evolving scalar fields significantly ease this tension by adding energy to the Universe around recombination in a narrow redshift window. We identify solutions of $V propto phi^{2 n}$ with simple asymptotic behavior, both oscillatory (rocking) and rolling. These are the first solutions of this kind in which the field evolution and fluctuations are consistently implemented using the equations of motion. Our findings differ qualitatively from those of the existing literature, which rely upon a coarse-grained fluid description. Combining CMB data with low-redshift measurements, the best fit model has $n=2$ and increases the allowed value of $H_0$ from 69.2 km/s/Mpc in $Lambda$CDM to 72.3 km/s/Mpc at $2sigma$. Future measurements of the late-time amplitude of matter fluctuations and of the reionization history could help distinguish these models from competing solutions.
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