A compressor is the right answer. If you lean toward more old-school audio engineering, I would recommend one of these compressors:

* Alesis 3630

* DBX 166 or 266

* FMR Audio Really Nice Compressor

Explore the various demos on YouTube to see what these are about. The compressor goes between your audio source and your amplifier. I personally use the Alesis 3630 for normalizing the audio in my ham radio transceiver setup.