Applying language models (LMs) to tables is challenging due to the mismatch between the two-dimensional structure of tables and the one-dimensional inputs expected by LMs. This mismatch forces linearization, making LMs particularly sensitive to irrelevant cells. Subtable selection mitigates this challenge by isolating question-relevant content prior to answer generation. However, existing approaches either rely on independent row or column selection, failing to capture cross-row and cross-column dependencies, or attempt global reasoning and face challenges similar to holistic table QA under noisy contexts. We propose *PieTa* (Piece of Table), a divide-and-conquer subtable selection framework that progressively aggregates locally selected evidence without requiring explicit global reasoning. *PieTa* uses an iterative, window-based multi-resolution process to construct compact subtables that capture global dependencies while limiting LM exposure to irrelevant content. Extensive experiments demonstrate that *PieTa* consistently outperforms prior subtable-based and holistic table QA approaches.