  We examine the recent work of de Rafael and Taron where model-independent
bounds on the Isgur-Wise function are presented. We first argue that the bounds
cannot hold in as much generality as implied. We show that the effects of
resonances omitted in their discussion (such as heavy-heavy ``onium'' states
below threshold) modify the bound. The resulting bound is much weaker but may
be useful where the size of the additional contribution may be computed or
estimated.
