Calming the mind to mushin, or “no mind.” Removing internal chatter to allow the mind to function more efficiently.
Nagamine Hanshi focused on achieving this state through the study and practice of Zazen and Zazen meditation.
Other Okinawa styles have incorporate the kata Sanchin. Sanchin, literally translates as "three battles" which refers to the development of mind, body and spirit.
Sanchin is a deceivingly simple kata, linear movements, basic block and punches incorporated into the sanchin dachi stance. The difficulty does not lie in the moves themselves but rather the single minded focus on tension and relaxation that accompanies the movements and centers on awareness of the breath.
If you are looking to expand your practice by incorporating a traditional Okinawan kata while retaining the focus of mindfulness consider adding Sanchin to your repertoire.
There are numerous resources for Sanchin with some variations from practitioner to practitioner. YouTube (below) has several clips.
Goju-Ryu Sanchin Kata By Morio Higaonna
Higaonna Sensei, Sanchin - Explanation and Training
Sanchin kata by Goshi Yamaguchi
Another excellent source is available from Tsunami Productions located at http://www.dragon-tsunami.org/Tsunami/Pages/go2rev.htm
All of this is not to say the process is easy or even attainable for everyone but it is another avenue for more fully developing the holistic karate-ka and not just the punching-kicking mindless karate "master" so many occidentals view themselves as.