  We consider a popular model for long-duration gamma-ray bursts, in which the
progenitor star, a stripped helium core, is spun up by tidal interactions with
a black- hole companion in a compact binary. We perform population synthesis
calculations to produce a representative sample of such binaries, and model the
effect that the companion has on material that falls back on to the
newly-formed black hole. Taking the results of hydrodynamic models of
black-hole formation by fallback as our starting point, we show that the
companion has two main effects on the fallback process. First, a break forms in
the accretion curve at around 10 000 s. Secondly, subsequent to the break, we
expect to see a flare of total energy around 0.1 foe. We predict that the break
time is set largely by the semi-major axis of the binary at the time of
explosion, and that this correlates negatively with the flare energy. Although
comparison with observations is non-trivial, we show that our predicted break
times are comparable to those found in the X-ray light curves of canonical
long-duration gamma-ray bursts. Similarly, the flare properties that we predict
are consistent with the late-time flares observed in a sub-sample of bursts.
