We report subarcsecond-resolution VLA imaging of the centers of four nearby spiral galaxies: IC 342, Maffei II, NGC 2903, and NGC 6946. In each galaxy, 7 - 12 compact radio continuum sources were identified within the central 15 x 15. Slightly over half of the compact sources appear to be HII regions with flat or positive spectral indices (alpha >~ -0.1). The HII regions with rising spectra are optically thick at centimeter wavelengths, and thus dense (n_i ~ 10^4 cm^(-3)) and young. The largest of these HII regions require the excitation of 500 - 800 O stars, within regions of only few parsecs extent. These clusters approach the sizes expected for globular clusters.