We study the evolution of hydrogen-rich cataclysmic variables (CVs) ne
ar minimum orbital period at similar to 78 minutes. As has been known
for many years, these are among the most intrinsically common CVs, but
they hide fairly well because of their faintness and low incidence of
eruptions. We discuss their number and observational signatures, payi
ng special attention to those that may have passed minimum orbital per
iod-the ''period bouncers.'' The status of binaries near minimum perio
d is best determined by the mass ratio, and this is best constrained b
y measuring the accretion disk precession frequency, because that freq
uency is readily accessible to observation and proportional to the sec
ondary star's mass. This method reveals four stars that are good candi
dates to have survived period bounce; two appear to have secondaries a
s puny as 0.02 M-.. But each star can have bounced only recently if at
all. There is still no strong evidence of any long era of evolution i
n a state of increasing period. This conflicts sharply with discussion
s of observational data that have identified dozens of known CVs with
this state. The total space density of cataclysmic variables is simila
r to 10(-5) pc(-3), with short-period systems constituting similar to
75% of the total. Both estimates are far less than predicted by simple
theories of evolution. It is probably necessary to have some means of
destroying CVs before they reach the predicted very high space densit
ies. This can be done by invoking an angular momentum loss mechanism t
hat does not quickly subside as the mass ratio becomes very low.