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 less than or similar to 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 minute periodic modulation of the visible flux of semiamplitude 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 four of the seven globular cluster X-ray sources with constrained periods are ultracompact, a fraction far greater than that found in X-ray binaries the field.