Testing configurable systems continues to be challenging and costly. Generation of configurations for testing tends to use either techniques based on semantic sampling (e.g., logical formulas over configuration variables, often called presence conditions) or structural code metrics (e.g., code coverage). In this paper we describe our hybrid approaches that combine these two kinds of techniques to good effect. We present new configuration-generation algorithms that leverage constraint solving (SAT and MaxSAT) and configuration fuzzing, and implement our approach in a configuration-generation framework, CONFIZZ. CONFIZZ both enables the generation of maximal configurations (maximal sets of presence conditions that can be satisfied together) and performs code-metric guided configuration fuzzing. Results from evaluation on BusyBox, a highly configurable benchmark, show that our MaxSAT-based configuration generation achieves better coverage for several code metrics. Results also show that, when high coverage of multiple configurations is needed, CONFIZZ's presence-condition fuzzing outperforms alternatives.