I've got some footage which was shot on Sony Z7, in dim light, with high gain.

The footage is slightly grainy - especially brown noise in the black areas.

I heard once that you can "crush blacks in post", to improve this. Can anyone elaborate on what this means, and how to achieve with Premiere CS3?

In levels, or fast color corrector, drag the left-most arrow of the input control towards the right - you will see the brown noise turn black. Then adjust the middle arrow as needed.

Using Curves instead of Levels will make more natural gradients and shadows, but yes - crushing blacks means severely compressing their luma range.

Thanks Graham and Jiri - got it! Works a charm! Thank you!