We present multifrequency radio continuum observations, made with ATCA, of a sample of 15 southern hemisphere luminous IRAS point sources, all with colors typical of compact H II regions and associated with CS (2 → 1) emission. The sources were observed at 1.4, 2.5, 4.8, and 8.6 GHz with angular resolutions of about 7'', 4'', 2'', and 1'', respectively. Radio emission was detected toward 14 objects. Nine IRAS objects are associated with single regions of ionized gas with simple morphologies; three are associated with two regions of ionized gas, each of which also shows simple morphologies, and two are associated with regions of ionized gas that have complex structure. The H II regions with simple morphologies have linear diameters in the range 0.011-0.9 pc and electron densities in the range 103-105 cm-3 and are excited by stars with luminosities in the range 9 × 103-2 × 105 L☉. We find that the H II regions in our sample, most of which lie at the center of massive and dense molecular cores with H2 densities of ~4 × 105 cm-3 and line widths of ~3 km s-1, are excited by stars with an output of UV photons of typically ≤3 × 1048 s-1. Under these conditions the regions of ionized gas reach pressure equilibrium with the dense molecular surroundings in only ~5 × 103 yr. We conclude that the main mechanism of confinement of the compact H II regions in our sample is provided by the high density and large turbulent pressure of the surrounding molecular gas; therefore, their age can be much longer than their dynamical timescale. If the objects in our sample are representative of the Galactic IRAS sources with colors of compact H II regions, then the problem with the large rate of massive star formation in the Galaxy might be solved.