My workflow for this sort of thing is as follows.
1. Compression. Use a good compressor to automatically roll off the louder bits thus allowing you to set the basic level higher which makes the quieter parts not so quiet while keeping the loud bits from getting out of hand.
2. Brick wall limiting. If compression isn't enough to get it done, I add a limiter. This prevents the loudest bits from being any louder than most of the much quieter bits. Used with compression, you can effectively control the volume of most source material while still achieving a relatively natural sounding result.
3. If compression and limiting don't get it done, I bring up the rear with fader automation for the worst bits. Sometimes the fader I automate is the volume fader. Sometimes its one or more eq bands. Whatever it takes to get it done in a natural sounding way.