We present a refined method for creating orbits of fictitious Earth impactors that are representative of the actual impactor population. Such orbits are crucial inputs to a variety of investigations, such as those that seek to discern how well and how early a particular asteroid survey can detect impactors, or to understand the progression of impact probability as an object is tracked after discovery. We will describe our method, which relies on Öpik's b-plane formalism, and place it in context with previous approaches. While the Öplk framework assumes the restricted three body problem with a circular Earth orbit, our final synthetic impactors are differentially corrected to ensure an impact in the N-body dynamics of the solar system. We also test the validity of the approach through brute force numerical tests, demonstrating that the properties of our synthetic impactor population are consistent with the underlying Near-Earth Object (NEO) population from which it is derived. The impactor population is, however, distinct from the NEO population, not only by virtue of the proximity of the asteroid orbit to that of the Earth, but also because low encounter velocities are strongly favored. Thus the impacting population has an increased prominence of low inclination and low eccentricity orbits, and Earth-like orbits in particular, as compared to the NEO population as a whole.