Can you tempo tighten a tempo mapped project?

Let's say you play something free form, then use "Fit to Improv" or manually with "Set Measure Beat at Now" function to created a tempo map that conforms to what you play. 
 
Once this is done, is there any way to tighten up the timing of the song/tempo map? Let's say the tempo swings from a low of 115 BPM to a high of 125 BPM. Is there anyway to change it to swing from 118 to 122?
 
Getting ready to work on a new live recording. Trying to determine whether to align the song to the grid or the grid to the song. If I align grid to song, I might still want to tighten up the timing of it a bit, but I haven't figured out a way to do that. Seems like once I align the grid to the song, I'm sort of stuck with the timing.
 
In the past, I've always aligned the song to the grid, then I have options for groove quantize or quantize strength settings to keep some of the feel in the song. Not sure I have those options if I align the grid to the song. 
 
gabo

It is very difficult to create a tempo map to an existing track, that matches perfectly.  Louder sections tend to drift up in tempo and more quiet section tend to drift down in tempo (in the real world) and getting these tempos to drift exactly to the music is very difficult.
 
If you are doing mostly MIDI tracks, I agree with Mr. Brundlefly's work flow. If you are trying to add MIDI tracks to existing audio tracks and want TIGHTNESS, the only way I know how to do this is to slowly edit the TEMPO map to the live audio tracks and tweak until it is close enough.
 
Hope this helps you.  I remember a band called the Moderns from NJ, I was in a band called The Plugs and we used to play in the same club circuit.  Is that your band by any chance?
 
Jim

I use Set Measure/Beat with audio as well. It takes a little more time to get things exactly right because you can't count on tab-to-transient to put the Now time right on the money as you can with MIDI. Otherwise the process is the same and gives very good and precise results - much better and faster than I can imagine achieving by manually entering tempo changes and tweaking them by trial and error. 

I probably should have mentioned that you can do what I call "flattening" the tempo map with audio just as well after aligning the timeline with Set Measure/Beat. You just need to enable Audiosnap in Autostretch mode on the clips before making any changes. The results are likely to be a lot more natural-sounding than trying to partially quantize to a fixed grid, which is almost impossible if the tempo is moving around much at all. And if you're working with multiple tracks, the beauty of this approach is that the tracks will all maintain sync and phase without having to jump through all the hoops of locking and merging markers across tracks because the tempo map acts as a sort of 'global marker set' that's shared by everything in the project.

The NJ guys were like us, human juke boxes.... the legal drinking age was lowered to 18 and it was like a party every night.  There were about 50 clubs within a 25 mile radius between North Jersey and NYC and a lot of the clubs had LIVE bands 7 nights a week (including the Jersey shore in the summer).  It was one giant PARTY back then.
 
Jim