I also really like the below exercise. String Specific Barre Correction – Try to apply pressure to the specific string indicated (not across the entire barre). Let the specified note ring cleanly while letting the notes marked with an X but muted (the barre finger is touching the string but not applying pressure to the fret. Don’t worry if the surrounding strings get pushed down as well (this is normal), just do your best and try to zero-in on the specified string. Keep fingers 2, 3 and 4 hovering over the frets where they would usually play (one finger per fret).
I play a little bit of jazz on the side and the barre chords are great practice if you use a pressure-release style of strumming (Freddie Green!). To do this, strum a barre chord and release of the pressure in the left hand immediately after. Release the pressure but do not remove your fingers from the strings (touch the strings but do not push down to the fret). This will mute the sound giving a very rhythmic feel that is very suitable to swing music.