Zou, Y. and Weglein, A.B., 2014. The internal-multiple elimination algorithm for all reflectors for 1D earth. Part I: strengths and limitations. Journal of Seismic Exploration, 23: 393-404. The ISS (Inverse-Scattering-Series) internal-multiple attenuation algorithm can predict the correct time and approximate amplitude for all internal multiples without any subsurface information. In practice, an energy minimization adaptive subtraction step is often called upon to then remove the residual/attenuated internal multiple. However, the energy minimization criteria behind the adaptive subtraction algorithm can fail with interfering or proximal primary and multiple events. The latter can occur with complex off-shore plays and very often occurs with on-shore plays. In 2003, Weglein proposed a three-pronged strategy for providing an effective response to this pressing and prioritized challenge. One part of the strategy is to develop an internal-multiple elimination algorithm that can predict both the correct amplitude and correct time for all internal multiples. The ISS internal- multiple elimination algorithm for all first-order internal multiples generated from all reflectors in a ID earth is proposed in part I of this paper. The primaries in the reflection data that enters the algorithm provides that elimination capability, automatically without our requiring the primaries to be identified or in any way separated. The other events in the reflection data, that is, the internal multiples, will not be helpful in this elimination scheme. That is a limitation of this new algorithm. In part II, we show that we can replace all bi in the elimination algorithm by bi + by to mitigate this limitation. Moreover, this elimination algorithm based on the ISS internal-multiple attenuation algorithm is derived by using reverse engineering to provide the difference between eliminate and attenuate for a 1D earth. This particular elimination algorithm is model type dependent since the reverse engineering method depends on the specific relationship between reflection and transmission coefficients for an acoustic medium. The ISS internal-multiple attenuation algorithm is model type independent. Future work will pursue the development of an eliminator for a multi-dimensional earth by identifying terms in the inverse scattering series that have that purpose and capability.