user108: It appears that I have found it possible to focus both on the breath (as a meditation object) and to be aware of a bit of a train of thought. 
Is this acceptable, or unacceptable, or should it be avoided? Or, is it perhaps simply varying "snippets" of mind-moments where I am slipping in and out of bare awareness of the meditation object?

user4753: I'd say that if you multi-task, acknowledge multi-tasking (which is at that moment on top of both breath and thoughts), let it go, and return to the breath. And see what happens in the next moment.
Perhaps when you multi-task, there is also a reason underneath that (avoiding some difficult feelings or pain, ambition to meditate "well", avoidance of boredom or tiredness) which you can become aware of (not by analyzing, just by looking), -- then acknowledge that one, let it go, and return to the anchor.
If you are aware of the snippets of mind-movements as they are alternating, acknowledge that awareness, and perhaps any induced reaction (liking, disliking, fascination, thoughts, comparison), let it go, and return to your anchor (breath).

user4722: Multi-tasking is an illusion... I have read that the mind and the senses are like a monkey sticking its head out six different windows rapidly in succession.  
A great lama once told me that trying to solve a puzzle when you sit down to meditate is in actuality making another samsara.

108: <p>It appears that I have found it possible to focus both on the breath (as a meditation object) and to be aware of a bit of a train of thought. </p>

<p>Is this acceptable, or unacceptable, or should it be avoided? Or, is it perhaps simply varying "snippets" of mind-moments where I am slipping in and out of bare awareness of the meditation object?</p>
 4753: <p>I'd say that if you multi-task, acknowledge multi-tasking (which is at that moment on top of both breath and thoughts), let it go, and return to the breath. And see what happens in the next moment.</p>

<p>Perhaps when you multi-task, there is also a reason underneath that (avoiding some difficult feelings or pain, ambition to meditate "well", avoidance of boredom or tiredness) which you can become aware of (not by analyzing, just by looking), -- then acknowledge that one, let it go, and return to the anchor.</p>

<p>If you are aware of the snippets of mind-movements as they are alternating, acknowledge that awareness, and perhaps any induced reaction (liking, disliking, fascination, thoughts, comparison), let it go, and return to your anchor (breath).</p>
 4722: <p>Multi-tasking is an illusion... I have read that the mind and the senses are like a monkey sticking its head out six different windows rapidly in succession.  </p>

<p>A great lama once told me that trying to solve a puzzle when you sit down to meditate is in actuality making another samsara.</p>
