hope you don't mind me jumping in Fred.
Alistair, the two sources of noise being considered here are read noise and shot noise from sky radiation.
The read noise is a burst of noise that you get on every read of data from a pixel - you can't do anything to reduce it, except by reducing the number of reads you perform (ie use very few long subs). The shot noise is determined by random arrival times of photons - it turns out that the signal to noise ratio due to shot noise is just the square root of the signal and the shot noise therefore increases as you increase the total detected signal. However, you are better off to have more signal, since the signal level increases more rapidly than the associated shot noise.
The read noise has a fixed average power, so if you can increase the signal, you eventually reach the point where the shot noise (and the signal) has gone up enough that the read noise becomes relatively insignificant in the total noise. At this point, all you are left with (practically) is signal and shot noise and that is as good as gets. The way to get more signal is to integrate longer - ie use longer subs. You do not want to use subs that are too long though, because you start filling up the wells on the chip and dynamic range suffers. To improve the signal to noise ratio once you have got to the point where shot noise is the limiting factor, you can add more subs - that way you get better signal to noise ratio without messing up the dynamic range and the shot noise will still be dominant over the read noise.
If the sky is bright, you will get more background signal in a given time, so you can use shorter subs and still have enough signal to overwhelm the read noise. the read noise does not change of course.
If the sky is really dark and you are using a narrow-band filter, there may not be much sky signal at all and you will need really long subs to get enough signal that the shot noise will overwhelm the read noise. The sky brightness makes no difference to the read noise, but it does determine how much effect the read noise has on the signal to noise ratio for a given sub exposure length.
have a read of this and look at the section on sky limited exposure and the references in that section.
http://starizona.com/acb/ccd/advtheoryexp.aspx
Re the question of what is signal and what is noise, the limiting noise in astro images is not in the bright bits - you are always trying to extract slight signals without making the sky background noise too objectionable - ie it is the noise in the background sky bits that determines how much of the dim stuff you can extract and background noise is what the analysis is all about. If you have a really bright object and don't care so much about background noise, use shorter subs.
Of course, the whole point of the suggested method is that it takes care of the details - you just have to remember one easily calculated ADU number and aim for it in your imaging. That's what I will be doing from now on.
regards Ray