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We use the large spectroscopic data set of the MOSFIRE Deep Evolution Field survey to investigate some of the key factors responsible for the elevated ionization parameters ( U ) inferred for high-redshift galaxies, focusing in particular on the role of star-formation-rate surface density (Σ _SFR ). Using a sample of 317 galaxies with spectroscopic redshifts z _spec ≃ 1.9–3.7, we construct composite rest-frame optical spectra in bins of Σ _SFR and infer electron densities, n _e , using the ratio of the [O ii ] λ λ 3727, 3730 doublet. Our analysis suggests a significant (≃3 σ ) correlation between n _e and Σ _SFR . We further find significant correlations between U and Σ _SFR for composite spectra of a subsample of 113 galaxies, and for a smaller sample of 25 individual galaxies with inferences of U . The increase in n _e —and possibly also the volume filling factor of dense clumps in H ii regions—with Σ _SFR appear to be important factors in explaining the relationship between U and Σ _SFR . Further, the increase in n _e and SFR with redshift at a fixed stellar mass can account for most of the redshift evolution of U . These results suggest that the gas density, which sets n _e and the overall level of star formation activity, may play a more important role than metallicity evolution in explaining the elevated ionization parameters of high-redshift galaxies.