It is very important to resolve the longstanding conflicts in the neutron-activation analysis (NAA) data on the bullets and fragments from the 1963 assassination of President John F. Kennedy and to understand their true meaning for the assassination. The five basic bullets and fragments, first analyzed in secret by the FBI in May 1964 and then in public by Vincent P. Guinn in September 1977, can potentially provide important information about the number and origin of bullets that hit Kennedy and Governor John B. Connally of Texas. While both sets of analyses appeared to divide the fragments into two physically meaningful groups that corresponded to two bullets, the body shot and the head shot, the FBI set was plagued by a serious systematic error and Guinn’s results from quarters of test bullets showed that the indicator element antimony varied enough over quarters to potentially invalidate the two-group interpretation by smearing the groups into one another. The contradiction can be removed by using the FBI results, which show that antimony is nearly homogeneous on the small scales of fragments, and by the actual mechanism by which jacketed bullets break when hitting bone, which generates tiny fragments from a single break near the middle of the lead core. Thus the fragments within each group were most likely produced near one another. The heterogeneities over quarters of cores then do not apply, and the two groups are as they appear. Once this is accepted, many other important pieces of the physical evidence fall into place and verify the original simple, straightforward picture of two and only two bullets from Lee Harvey Oswald’s rifle striking the two men.