Two or three relatively small branches have no bark left, except for the underside of those branches that are more horizontal than vertical. Is this a disease? The tree is long established and maybe about 70-80 feet tall. These branches are well above the height that deer can reach, unless they've learned to climb trees.

Greetings Armine:

Unfortunately, I can't tell by your description whether this bark loss is natural, environmental, or related to biological factors. I wouldn't worry too much if the limbs are small in diameter and few in number--it is common for tree branches to die, lose bark, fall to the ground, etc. Factors that cause this may include environmental factors such as wind, shading, mechanical damage, drought; biological factors such as insect, pathogens, or wildlife damage, etc.

I would not be worried based on your description of an 80-ft tall tree with a couple dead, small diameter branches.