  There are four puzzles on 1E 1207.4-5209: (1) the characteristic age of the
pulsar is much higher than the estimated age of the supernova remnant; (2) the
magnetic field inferred from spin-down is significantly different from the
value obtained from the cyclotron absorption lines; (3) the spinning down of
the pulsar is non-monotonic; (4) the magnitude of the frequency's first
derivative varies significantly and its sign is also variable. The third puzzle
can be explained by a wide binary system, with orbital period from 0.2 to 6 yr.
This letter proposes that all four puzzles can be explained naturally by an
ultra-compact binary with orbital period of between 0.5 and 3.3 min. With the
shortest orbital period and a close distance of 2 kpc, the characteristic
amplitude of gravitational waves is $h\sim3\times10^{-21}$. It would be an
excellent source of gravitational-wave detectors such as the Laser
Interferometer Space Antenna.
