Even Up words in speech

Hi, I have a movie sound track which contains an actor making a speech. Unfortunately, his voice goes up and down in volume much of the time.
Is there any way I can even up the speech, please? I want to keep to the same overall volume as the rest of the sound track. How might I do this on my Windows 7 pc? Audacity version: 2.1.0.
Would Compression be the solution, or is there something better?

The best method is usually the [u]Envelope Tool[/u] to manually fade-up and fade-down the sound. (And the “trick” is to fade without making any sudden changes.) It’s time consuming but you have full control over what’s happening.

Compression and/or limiting should help. There is also a [u]Leveler[/u] effect (a subset of the “distortion” effects). (Limiting is a kind of fast compression and leveling or automatic volume control is a kind of slow compression.) Or, there is also a stand-alone program called [u]The Levelator[/u] that might be worth a try.

The problem, no matter how you do it, is that when you increase the volume you also increase the background noise and sometimes that can be annoying/distracting.

There’s an app for that: an Audacity plugin, LevelSpeech2.ny

NB: If there are other sounds while the actor is speaking, (e.g. music), inevitably they will be modified too.

Thank you to both replies. They are both a help.
I tried with the Compressor but I am alarmed that the audio signal grows very big, ie, very loud! Too loud! I like to have all of my sound tracks to the standard 89db. Any suggestions how I can maintain them at 89db, after applying Compression or Hard Limiter?
Thank you again.