Hearing aid compression is typically designed for speech, yet music demands different trade-offs due to its narrower dynamic range (DR) and impulsive transients. This paper investigates whether music fitting benefits from being signal-aware, both in mapping compression demand across signal–audiogram conditions and in tuning its parameters to these combinations rather than inheriting them from speech-derived prescriptions. Compression demand is characterized across eight audiometric profiles, three residual DR severities, and three produced music signals under linear gain. Signal dynamics emerge as a first-order factor: production-compressed music fits the residual DR of the mild-to-moderate profiles evaluated, while dynamically rich recordings challenge even moderate hearing loss. Per-signal optimization of single- and multi-band wide dynamic range compression is then applied to two profiles with the highest compression demand. This optimization improves the Hearing Aid Audio Quality Index over gain-optimized NAL-NL2 baselines while also improving audibility, indicating substantial headroom for music-specific fitting.