The noise reduction tools in the newer versions of Lightroom are very powerful, although getting the most of them takes some work, as there are a lot of options. I once read a wonderful, detailed tutorial on using them, but I can't find it. However,
here is a brief explanation of the various tools.
Without getting into the fine points, one can often get very good results simply by doing this:
1. Blow the image up to 300% or 400%.
2. Use the color noise slider (just the top one) if needed. I find I rarely need it.
3. Drop down to 100%
4. Gradually move the top luminance slider until you smooth out noise without removing too much detail
You can then play with the detail slider. I find that it is usually fine where it is by default.
In my experience, that's often enough.