Evidence is emerging that the luminous X-ray sources in the cores of globular clusters may often consist of, or perhaps even as a class be dominated by, ultracompact (P < 1 hr) binary stars. To the two such systems already known, in NGC 6624 and NGC 6712, we now add evidence for two more. We detect large amplitude variability in the candidate optical counterpart for the X-ray source in the core of NGC 6652. Although the available observations are relatively brief, the existing Hubble Space Telescope data indicate a strong 43.6 min periodic modulation of the visible flux of semi-amplitude 30%. Further, although the orbital period of the source in NGC 1851 is not yet explicitly measured, we demonstrate that previous correlations of optical luminosity with X-ray luminosity and accretion disk size, strengthened by recent data, strongly imply that the period of that system is also less than 1 hr. Thus currently there is evidence that 4 of the 7 globular cluster X-ray sources with constrained periods are ultracompact, a fraction far greater than that found in X-ray binaries the field. Comment: 10 pages including 2 figures and 1 table. Accepted for publication in The Astrophysical Journal Letters