We prove that every topological dynamical system (X, T ) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y, S) such that for every S-invariant measure ν on Y the conditional entropy h(ν|X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y . This is a strengthening of the result in [D-H] (in which the extension was principal, but not necessarily faithful).