Parametric generators are a simple way to combine coverage-guided and generator-based fuzzing. Parametric generators can be thought of as decoders of an arbitrary byte sequence into a structured input. This allows mutations on the byte sequence to map to mutations on the structured input, without requiring the writing of specialized mutators. However, this technique is prone to the \emph{havoc effect}, where small mutations on the byte sequence cause large, destructive mutations to the structured input. This registered report first provides a preliminary investigation of the paradoxical nature of the havoc effect for generator-based fuzzing in Java. In particular, we measure mutation characteristics and confirm the existence of the havoc effect, as well as scenarios where it may be more detrimental. The proposed evaluation extends this investigation over more benchmarks, with the tools Zest, JQF’s EI, BeDivFuzz, and Zeugma.