In continuous-variable systems, quantifying the structural complexity of quantum states is crucial for distinguishing trivial classical-like configurations from genuinely quantum features. Here we propose a family of phase-space complexity measures, termed Rényi-Wehrl-Fisher complexities, for single-mode continuous-variable quantum states. This family integrates global delocalization from the Rényi-Wehrl entropy and local sharpness from the Fisher information. Notably, we establish a universal lower bound saturated if and only if the state is displaced thermal. The measure is invariant under phase-space displacements, rotations, and uniform scalings and recovers the previously introduced Wehrl-Fisher complexity when the Rényi parameter approaches unity. The tunable Rényi parameter acts as a phase-space selector. On the one hand, it amplifies low-probability tails where quantum interference resides or highlights the high-probability core where the bulk of the distribution concentrates. This tunability reveals a fundamental dichotomy hidden in the fixed Shannon-entropy framework. Moreover, the complexity is strictly parameterindependent for all Gaussian states but acquires strong parameter dependence for non-Gaussian states. This dichotomy enables an experimental diagnostic. By tuning the parameter in heterodyne measurements, one certifies non-Gaussianity in a self-calibrating manner. We derive closed-form Fock-state expressions. The complexity distinguishes squeezed states with unbounded range, detects cat-state coherence where the fixed measure is blind, and captures entropy-Fisher competition in mixed non-Gaussian states. These results establish the Rényi-Wehrl-Fisher complexity as a rigorous, experimentally accessible, and versatile tool for characterizing structural complexity and quantum nonclassicality in continuous-variable systems.

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• Quantum Fisher information
• Quantum harmonic oscillator
• Quantum information theory