Gil Fronsdal leads a Guided Meditation Dharmette: A short instruction being mindful, Abide Conscious not Self Conscious. Be Conscious, not Self Conscious.
It's possible to be aware, without the static or agitation of self preoccupation, means too caught up or self-concern, or being too self-conscious. Being pulled-in or caught up in own little inner drama of self-preoccupation that we're not really present and available or smooth and fluid in how we live our lives.
To get a sense of, to see how self-consciousness works is in fact one of the purposes of Mindfulness practice. Without seeing what we do, there's no possibility of moving through it or healing from it. or being wise about it. And instead of the static or agitation of being self-conscious, to dwell conscious, to dwell aware, be mindful, to open up into a field of awareness that in a sense hold it all.