In many instances resonance capture of neutrons can be calculated by one of two basic approximations. The narrow resonance approximation is valid if the practical width is small compared with the maximum energy loss of a neutron in an elastic collision. If the reverse is the case, the absorber atoms may be regarded as infinitely heavy. There are cases of wide, weakly absorbing, resonances however in which neither of these methods is reliable. Examples of these are given. An alternative method for calculating resonance capture for such resonances is presented and compared with Monte Carlo calculations of the capture fraction in bismuth-graphite lattices.