The thesis defended is that at a certain arbitrary level of granularity, mountains have sharp, bona fide boundaries. In reply to arguments advanced by Varzi (2001), Smith & Mark (2001, 2003) I argue that the lower limit of a mountain is neither vague nor fiat. Relying on early works by Cayley (1859), Maxwell (1870) and Jordan (1872), this lower limit consists in the lines of watercourse which are defined as the lines of slope starting at passes. Such lines are metaphysically sharply delineated although they are not always easy to get at when facing a mountain. Hence, the indetermination is only epistemic. In the second part of the paper, I try to combine this claim about the lower limit of a mountain with more recent claims advanced by alpinists on the right way to measure the height of a mountain, so as to capture its topographic prominence. I argue following them that the proper height of a mountain is the difference of altitude between its summit and its key-saddle, defined as the highest saddle one needs to cross in order to reach the closest higher summit. Combining this two plausible views about the lower limit and height of a mountain leads to the surprising result that the key-saddle needed to measure the height of a mountain is not necessarily located on the lower-boundary of that mountain.