  We describe a conjectural stratification of the Brill-Noether variety for
general curves of fixed genus and gonality. As evidence for this conjecture, we
show that this Brill-Noether variety has at least as many irreducible
components as predicted by the conjecture, and that each of these components
has the expected dimension. Our proof uses combinatorial and tropical
techniques. Specifically, we analyze containment relations between the various
strata of tropical Brill-Noether loci identified by Pflueger in his
classification of special divisors on chains of loops.
