In regards to what you wrote TMingyur and in terms of using mindfulness to tame the mind how would this actually be done in practice?
I like to be diligent in practicing mindfulness but sometimes the mindfulness itself leads to things like tension or there will still be a lot of discursive thoughts going on and not much calm.
There are different approaches as to mindfulness depending on the view that is the basis of this mindfulness.
In principle "being mindful" implies seeing all phenomena that appear to/in the mind in a manner that is conducive to wisdom and/or liberation from suffering. Phenomena that appear to the mind comprises both "outer" and "inner" phenomena.
What are different ways of conducively seeing?
Just two examples (there are actually much more ways)
1. First of all there is the "classical" way as taught by the Buddha in the Satipatthana Sutta
2. Next there might be the knowledge of Madhyamaka emptiness being present in one's mind and being applied spontaneously to all appearing phenomena. This refers to the post-meditation awareness that there is nothing that is ultimately real. This is commonly referred to metaphorically as "seeing all phenomena as if it were in a dream".
Both ways actually entail the same: Not clinging to appearances and this "not clinging" avoids "getting caught up in appearances" and the unwholesome states of minds that result from this.
The prerequsites for all kinds of mindfulness is a mind that is neither agitated nor sleepy but has clarity and vigor. And the prerequites for these prerequisites is a way of living that accords with the Buddha's teachings: Ethics, restraint from sensual pleasures/desire, appropriate diet, appropriate balance of sleep and waking, practicing love/compassion ... etc.
And of course: right effort (i.e. practicing) and joyous perseverance which is based on faith and knowing the advantages of the goal attained through that practice.
Practice of concentration, i.e. concentrative meditation (shamata) is a means to foster the capacity for mindfulness.
Practice "thinking about" and "analyzing" after having attained at least some level of "calmed mind" (shamata) is a means to get to "know" (attain some insight into) the conducive way of seeing applied in mindfulness.