Long-context DNA models are limited by token-mixing cost and by how compression allocates representational budget across the genome. Existing approaches operate close to base-pair resolution, apply fixed downsampling, or learn content-dependent chunks without an explicit genomic budget, making long-context pretraining expensive and difficult to control. We introduce GeneZip, a region-aware DNA compression framework that combines H-Net-style dynamic routing with a Region-Aware Ratio (RAR) objective and bounded routing. GeneZip uses static gene-structure annotations during compression training to specify region-wise base-pairs-per-token (BPT) targets; at inference time, it compresses raw unseen DNA without annotations. GeneZip provides three main benefits. First, it is effective: GeneZip variants achieve the best validation PPL among encoder-based compressors, with GeneZip-70M operating at 137.6 BPT, and across four reproducible DNALongBench tasks--contact map prediction, eQTL prediction, enhancer-target gene prediction, and transcription-initiation signal prediction--GeneZip obtains the best average rank among compared sequence models. Second, it is redundancy-aware: a post-hoc RepeatMasker/TRF analysis shows that, without repeat supervision, GeneZip assigns higher local BPT to TE-derived interspersed repeats and tandem repeats, two major classes of repetitive DNA sequence redundancy. Third, it is efficient: by reducing the effective token-mixing length, GeneZip enables longer-context and larger-capacity pretraining, including 128K-context and 636M-parameter variants on a single A100 80GB GPU, and fine-tunes the eQTL task 50.4x faster than JanusDNA (50 vs. 2520 minutes). These results establish GeneZip as an effective, redundancy-aware, and efficient compression interface for long-context DNA modeling.