Those in the process of constructing a space that involves anything audio, will find that the best way to tighten up a room's sound and make it more soundproof is to design it right, build it tight (reduce air travel) and make the partitions as dense as possible.
The 4" Mineral Fiber Insulation from Auralex is specifically designed for acoustical usage and comes in 48 x 24 x 4" panels. It yields much better bass trapping, overall absorption, thermal characteristics, moisture absorption and sound transmission loss (isolation.) It is also denser than regular fiber insulation and rates better in retarding flame spread and smoke density, including a 1200° burn point vs. 650° for standard insulation.
4" Mineral Fiber Insulation provides absorption of frequencies between 250Hz and 4kHz, similar to the 2" panels, but is dramatically more effective at 125Hz. Additionally, 4" insulation will offer higher levels of STL (Sound Transmission Loss) than will 2" due to the increased mass 4" offers.