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 (ΣSFR). 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 ΣSFR and infer electron densities, n e, using the ratio of the [O ii] λ λ3727, 3730 doublet. Our analysis suggests a significant (≃3σ) correlation between n e and ΣSFR. We further find significant correlations between U and ΣSFR 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 ΣSFR appear to be important factors in explaining the relationship between U and ΣSFR. 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.