  Gravitational radiation arising from the inspiral and merger of binary black
holes (BBH's) is a promising candidate for detection by kilometer-scale
interferometric gravitational wave observatories. This paper discusses a
serious obstacle to searches for such radiation and to the interpretation of
any observed waves: the inability of current computational techniques to evolve
a BBH through its last ~10 orbits of inspiral (~100 radians of
gravitational-wave phase). A new set of numerical-relativity techniques is
proposed for solving this ``Intermediate Binary Black Hole'' (IBBH) problem:
(i) numerical evolutions performed in coordinates co-rotating with the BBH, in
which the metric coefficients evolve on the long timescale of inspiral, and
(ii) techniques for mathematically freezing out gravitational degrees of
freedom that are not excited by the waves.
