Black-box context-free grammar inference is a hard problem as in many practical settings it only has access to a limited number of example programs. The state-of-the-art approach Arvada heuristically generalizes grammar rules starting from flat parse trees and is non-deterministic to explore different generalization sequences. We observe that many of Arvada's generalization steps violate common language concept nesting rules. We thus propose to pre-structure input programs along these nesting rules, apply learnt rules recursively, and make black-box context-free grammar inference deterministic. The resulting TreeVada yielded faster runtime and higher-quality grammars in an empirical comparison. The TreeVada source code, scripts, evaluation parameters, and training data are open-source and publicly available (https://doi.org/10.6084/m9.figshare.23907738).