Hi Bob!
Actually - don't look at the peak, that is showing you where most of the tonal values are. Instead you want to look at the edges. See how the histogram approaches, but doesn't go over, the right side? These are the highlights and it is important to try to get this as close to that right edge as possible, without going over the edge. In this instance, I wouldn't add any additional compensation as any more would likely push it over, which is known as "clipping". Once the data goes over that edge, it is lost forever (actually the histograms are based on JPEG images, so if you are shooting RAW, you do have a little more room!!).
The same applies to the left side, but the way photo sensors works (CCDs and CMOS chips), 50% of the detail is contained in the first stop from the right side. So, if you don't have any values up there due to an underexposure, you have thrown away 50% of the detail! The other 50% is contained in the remainder of the histogram.

- histogram
- histogram2.jpg (31.57 KiB) Viewed 24568 times
Hopefully this illustrates it better - I divided the histogram into the five stop range that it covers. The first stop on the right contains 50% of the detail - the remaining 4 stop contain the rest of the detail - the remaining 50%. So, if you don't have any luminance values in this upper section - you are not recording the maximum detail that you could be! However, you can go right up to that right hand edge, but no further as then you will be clipping, and in the case of the original white bird, you will lose detail and the resulting image will be pure white with no detail. This is OK for clouds, sun, bright lights, etc., but not something that you want to maintain detail!
Remember to view the histogram in the context of the scene that you are recording. If it is a dark scene, the histogram is going to have most of the peaks on the left, if it is a bright scene, most of the peaks will be on the right. The histogram above is likely that of a fairly average scene with an equal balance of bright and dark areas, so it looks like a bell-curve. The important thing is to record the brightest items that you wish to maintain detail go right up to that right edge, without going over.
By the way, if your camera has highlight warnings on the LCD (sometimes called the "blinkies"), this will also help show you what areas of the image have been clipped, or gone over the edge. Again, if it is something bright (like highlights or clouds, etc.) then I wouldn't be too concerned. However, if the white bird is flashing, then there will be no details in those feathers!
Does that help?