CERes is a method of cut-elimination that uses resolution proof search to avoid some kinds of redundancies that affect reductive cut-elimination methods. This article shows that, unfortunately, there are also cases where CERes can produce proofs that are more redundant and even exponentially larger than the proofs produced by reductive cut elimination methods. The article then describes a few novel variants of CERes that are much less susceptible to these redundancies. ; This work is supported by the Austrian Science Fund (FWF) projects P19875, P24300.