I experimented today with an alternative to severe burning that might be useful.
Sometimes, an area in a photograph is so light that the amount of burning necessary begins to turn the burned area gray. I had this experience again today with a candid of a toddler taken in available light, with light coming from the side. I was unable to darken the bright side of the face enough without introducing a gray tone. Unfortunately, I can't post the image that illustrates this because I never post publicly pictures of other kids.
The alternative uses photoshop's multiply blend mode. The way this works is that the pixel values on the two layers are multiplied to create the value in the blended image. So, it darkens, but using the colors that are in the layers.
My solution was this:
1. Duplicate the base layer, label the duplicate "multiply," and set the blend mode of the duplicate to multiply. The result will be to darken the image, but more in areas that are already dark than in areas that are initially light--the reverse of what's needed.
2. Add a black mask.
3. Paint white with 100% opacity but a very low flow, no more than 10%. Gradually build up the darkening effect where you need it. The low flow makes the results blend and also makes it easier to do more of this in the lightest areas, which will need the most correction given the way the blend mode works.
I had used a similar technique in the past, but to restore old faded photos, not for burning per se. For example, here is a faded photo of my great-grandparents, taken roughly in 1885. Note the lack of detail in my great-grandmother's face.
The following partially restored image entailed a lot of edits, but what I used for the faces and eyes was a multiply blend. Compare her face and eyes: