If dwarf-elliptical galaxies formed their stars very rapdily (on timescales of less than 1 Gyr), they may in principle be detectable out to high redshift. Prior to the discovery of cosmic acceleration, it appeared that rapid and late formation dwarf elliptical galaxies might be required to explain the number counts of faint galaxies. A plausible hypothesis emerged: that photoionization by the UV background prevents gas cooling in low-mass halos until $z \lesssim 1.5$. The discovery of cosmic acceleration eased the tension between predicted galaxy number counts and galaxy-evolution models. Nevertheless, there is some evidence for relatively late star formation in nearby dE's, and the photoionization delay mechanism still appears to have some merit. It is thus of interest to look back in time to see if we can find starbursting dwarf galaxies at moderate redshift. We review the connection between faint-blue galaxies and bursting-dwarf galaxies and discuss some attempts to identify progenitors to dE galaxies in the Hubble Ultra Deep Field (HUDF) observations. We find roughly 85 galaxies in the HUDF with redshifts $0.6<z<1.1$ that appear to have formed most of their stars at $z<1.5$. Of these, 70% have half-light radii less than 1.5 kpc. These are thus “smoking gun” candidates for dwarf galaxies that are either collapsing for the first time at moderate redshifts or have otherwise been unable to form stars for more than 1/3$ of a Hubble time.