It is demonstrated that the modified integration prescription given earlier for the elimination of unphysical asymptotic states in case of a theory with dipole regularization is equivalent to the Lee-Wick integration prescription for poles with complex mass if the dipole is considered as a limiting case of two merging poles, or more precisely, of two merging dipoles with complex conjugate mass. In particular, the thresholds of unphysical processes become points of nonanalyticity in the sense that the function left and right of these points cannot be connected by analytic continuation. The smoothness of this function at the nonanalytic points in the physical region essentially determines the fall-off of «acausal» precursors. It appears that with this procedure even ghost poles below the threshold of the continuum do not lead to a violation of unitarity.