  We show that a general curve in an explicit class of what we call Du Val
pointed curves satisfies the Brill-Noether Theorem for pointed curves.
Furthermore, we prove that a generic pencil of Du Val pointed curves is
disjoint from all Brill-Noether divisors on the universal curve. This provides
explicit examples of smooth pointed curves of arbitrary genus defined over Q
which are Brill-Noether general. A similar result is proved for 2-pointed
curves as well using explicit curves on elliptic ruled surfaces.
