  The discovery of two accreting millisecond X-ray pulsars in binaries with 43
minute orbital periods allows for a new probe of the donor's structure. For XTE
J1751-305, only a hot white dwarf (WD) can fill the Roche Lobe. A cold He WD is
a possible solution for XTE J0929-314, though I will show that evolutionary
arguments make a hot WD more likely. In addition to being larger than the T=0
models, these finite entropy, low-mass (<0.03 solar masses) WDs have a minimum
mass for a fixed core temperature. If they remain hot as they lose mass and
expand, they can ``evaporate'' to leave an isolated millisecond radio pulsar.
They also adiabatically expand upon mass loss at a rate faster than the growth
of the Roche radius if the angular momentum deposited in the disk is not
returned to the donor. If the timescale of the resulting runaway mass transfer
is shorter than the viscous timescale in the outer disk, then the mass transfer
instability of Ruderman and Shaham for He WDs would be realized. However, my
estimates of these timescales still makes the instability unlikely for
adiabatic responses. I close by noting the possible impact of finite T WDs on
our understanding of AM CVn binaries.
