The possibility of recriticality during the reflood phase of a severe accident in a boiling water reactor (BWR) is investigated. In addition, the fraction of control-rod material that must be retained to prevent recriticality is determined for several different geometries. Detailed calculations for a representative portion of a BWR core are performed with the Monte Carlo MCNP code to evaluate the neutronic response of the damaged core under a number of different scenarios. Retention of <10% of the 10B that is initially present in the control rods may be sufficient to prevent recriticality. The reactivity effect of the retained 10B is sensitive to the porosity and homogeneity of the eutectic formed by the control rod materials as well as to the degree to which that eutectic is dispersed inside the fuel bundles.