  We introduce four new molecules -- YbRb, YbCs, YbSr$^+$, and YbBa$^+$ -- that
may prove fruitful in experimental searches for the electric dipole moment
(EDM) of the electron. These molecules can, in principle, be prepared at
extremely low temperatures by photoassociating ultracold atoms, and therefore
may present an advantage over molecular beam experiments. Here we discuss
properties of these molecules and assess the effective electric fields they
contribute to an electron EDM measurement.
