It is pointed out that real-space images recovered from LEED I /E data by the current holographic reconstruction algorithm can contain strong artifacts which can be misinterpreted as atomic images (`ghost atoms'), thereby misguiding a subsequent structural refinement through conventional LEED. We show that such ghost atoms can be avoided by using an alternative approximation to the kernel in the reconstruction integral. This is demonstrated for both calculated and experimental intensities of the structure considered, i.e. a (2×2) phase of 6H-SiC(0001̅). A theory is also developed for a practical implementation of a more general kernel which fully takes account of the scattering of an electron by the substrate atoms before its first encounter with the adatom (beam splitter).