On a projective nonsingular curve C of genus g the variety N<sup>n</sup><sub>r</sub>(A) of neutral linear series parameterizes linear series of degree n and dimension r to which a given effective divisor A of degree s does not impose independent conditions. Edoardo Sernesi proved that, in the appropriate ranges of g,r,n,s, if C is a Brill-Noether curve then 
N<sup>n</sup><sub>r</sub>(A) is non-empty. As an application, here we deduce a Brill-Noether existence theorem for irreducible curves obtained from a Brill-Noether curve by identifying a pair of points to an ordinary node.