Deep learning has achieved strong performance in encrypted traffic classification (ETC), yet its computational cost limits deployment on resource-constrained network devices such as routers and middleboxes. Existing compression methods mainly operate on weights, channels, hidden representations, or predictions, but do not explicitly determine which protocol fields and structural contexts should remain. We propose Pruned Traffic Trees (PTT), a three-level protocol-structured model family that treats native protocol structures as compression units. PTT-Full learns protocol-structured representations and field salience from complete Protocol Tree Graphs (PTGs), with flow-level self-supervised learning and protocol-presence-aware sparse execution. The learned salience and TopK+$k$ closure construct Distilled PTGs (PTG-Ds) for PTT-Distilled, while PTT-Lite inherits this topology and reduces width through structure-aligned transfer and flow-level logits distillation. Under flow-disjoint and Strong Information Information (SII)-masked settings, PTT-Full achieves Macro-F1 scores of 0.9519 and 0.9416 on CSTNET-TLS1.3 and CipherSpectrum, while PTT-Lite retains 0.9325 and 0.9136 with 80.3\% and 61.3\% fewer parameters, 98.85\% and 98.78\% lower effective GFLOPs, and 8.75$\times$ and 8.46$\times$ CPU inference speedups. These results demonstrate that treating protocol structure itself as the compression object enables effective performance-efficiency trade-offs for lightweight ETC.

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