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In the application of a conventional common-reflection-surface (CRS) stack, it is well-known that only one optimum stacking operator is determined for each zero-offset sample to be simulated. As a result, the conflicting dip situations are not taken into account and only the most prominent event contributes to any a particular stack sample. In this paper, we name this phenomenon caused by conflicting dip problems as ‘dip discrimination phenomenon’. This phenomenon is not welcome because it not only leads to the loss of weak reflections and tips of diffractions in the final zero-offset-CRS stacked section but also to a deteriorated quality in subsequent migration.The common-reflection-surface stack with the output imaging scheme (CRS-OIS) is a novel technique to implement a CRS stack based on a unified Kirchhoff imaging approach. As far as dealing with conflicting dip problems is concerned, the CRS-OIS is a better option than a conventional CRS stack. However, we think the CRS-OIS can do more in this aspect. In this paper, we propose a workflow to handle the dip discrimination phenomenon based on a cascaded implementation of prestack time migration, CRS-OIS and prestack time demigration. Firstly, a common offset prestack time migration is implemented. Then, a CRS-OIS is applied to the time-migrated common offset gather. Afterwards, a prestack time demigration is performed to reconstruct each unmigrated common offset gather with its reflections being greatly enhanced and diffractions being well preserved.Compared with existing techniques dealing with conflicting dip problems, the technique presented in this paper preserves most of the diffractions and accounts for reflections from all possible dips properly. More importantly, both the post-stacked data set and prestacked data set can be of much better quality after the implementation of the presented scheme. It serves as a promising alternative to other techniques except that it cannot provide the typical CRS wavefield attributes. The numerical tests on a synthetic Marmousi data set and a real 2D marine data set demonstrated its effectiveness and robustness.