Hi Larry
Ok, now I get your point. Let's review a little about what this shape means.
Usually, in an astronomical image the feature that dominates, or that covers more space/pixels, is the background sky. The sky tends to use a small portion of the dynamic range, so it is safe to say that it should be pretty close to a constant value. If it were a single value signal, in a histogram it would be shown as a single, narrow peak, one for each channel. The position of each peak is related to the hue, or tone, of the sky, wich in turns depends on the device's sensibility, light pollution and many factors.
We said that an ideal sky background should be close to a narrow peak... but in the real world we see broad gaussian shaped bells. There are many reasons to this behavior. First, the sky itself is not flat at all. It varies dependind the alture (from the horizont) and from it's distance to the milky way. Also there are many subtle nebulosities that adds another sources to fluctuations. But in most cases, these are minor effects. Much more important is the uneven illumination, or vignetting. Also the noise itself expands the shape of the curve. So, if you want to get a tighter shape, you should use flats to calibrate the frames, remove any gradients from the sky due to light pollution and altitude, and later reduce noise.
If you are done with this, and want to further "fit" all the curves, you should use the Curves Transform... but, my recommendation is to forget the histogram shapes as soon as you balanced the peaks. It is more important how the image looks, and how the balance changes adjusting the curves than how statistically it is reflected on the histogram. You may end with nice histograms, but ugly images... wich is not your goal, I pressume. Also, remember that the right side of the shape contains all the information from the objects in your image (star haloes, nebulaes, DSO, etc), and theyr distribution may not be as neutral in hue as the background.
By the way, after we set the black and white points, usually we modify the middtones balance to make all three peaks to coincide at the same place, so the background gets a neutral tone (dark grey, or maybe a very deep blue, keeping the blue a bit to the right, followed by the green). Well, we introduced another process that may be a help for this task: AutomaticHistogram. It uses gama adjustments instead of rational interpolation, as in the HistogramTransform, so the results may differ in the highlights, or the contrast in the middtones (the shape of the histogram is tighter after a gama adjustment, compared to a rational interpolation). I recommend to check both adjustments and then choose wich gets better results in your case.