The paper introduces LOCUS, a post-training method that curbs verbosity in large language models by applying task-aware low-rank adaptations that identify a subspace minimizing output token cost while keeping the base model frozen. Evaluated on dialogue preference datasets using Pythia-2.8B and Qwen2.5-3B, LOCUS cuts continuation length by up to 39.84% while updating less than 0.3% of parameters, preserving preference-alignment quality. The approach targets practical inference-cost reduction rather than raw capability gains, making it applicable as a lightweight post-training step for deployed models.