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We show that every $3$-connected $K_{2,\ell}$-minor free graph with minimumdegree at least $4$ has maximum degree at most $7\ell$. As a consequence, weshow that every 3-connected $K_{2,\ell}$-minor free graph with minimum degreeat least $5$ and no twins of degree $5$ has bounded size. Our proofs useSteiner trees and nested cuts; in particular, they do not rely on Ding'scharacterization of $K_{2,\ell}$-minor free graphs.

A note on highly connected $K_{2,\ell}$-minor free graphs