In reply to:

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It seems to me that it would make more sense to increase the output of your amp slightly to make it so that you don't have to get into overdrive.

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Of course this is true, but if you already have your amps turned up to their maximum levels, then you don't really have anywhere to go other than overdrive, or possibly boosting the EQ levels.

At this point one might think that it was time for a bigger amp or more efficient speakers, but I feel that I should be able to get a little more volume out of the amps as my former head unit using the same amps delivered sound that was far louder than I would ever want.

This is only an issue for certian recordings, such as early Black Sabbath, some P.J. Harvey, things that seem quietier than most other recordings.

Perhaps the eaisest solution would be to edit these songs myself and crank them up a bit...?