  It is a well-known result that a stable curve of compact type over
$\mathbb{C}$ having two components is hyperelliptic if and only if both
components are hyperelliptic and the point of intersection is a Weierstrass
point for each of them. With the use of admissible covers, we generalize this
characterization in two ways: for stable curves of higher gonality having two
smooth components and one node; and for hyperelliptic and trigonal stable
curves having two smooth non rational components and any number of nodes.
