Wavelet convolution layers have recently emerged as an efficient mechanism for enlarging receptive fields through multiresolution analysis, but prior work has fixed the wavelet basis to Haar or Daubechies at a chosen decomposition depth, leaving open whether a different basis can shift the underlying efficiency frontier. We identify and characterize a previously unexplored trade-off in this setting: bases with stronger approximation properties (longer filters) can reduce the decomposition depth required for competitive accuracy, yielding a net reduction in parameters and FLOPs despite higher perlevel transform cost. We formalize this as an F-vs.-L tradeoff (filter length vs. decomposition levels) and study it systematically across Haar, Daubechies, Symlets, and Coiflets under controlled architectures and budgets. On image classification (CIFAR-10, ImageNet-1K) and semantic segmentation (Cityscapes), Coiflet-based wavelet convolutions match Haar at deeper levels with approximately 32% fewer additional parameters and 33% fewer additional FLOPs, providing a concrete and actionable design choice for practitioners building wavelet-based architectures.

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