Finsler spaces of $(\alpha,\beta)$ type and semi-C-reducibility

I clarify the definition of semi-C-reducibility for Minkowski norms and Finsler spaces, and give a streamlined proof of the fact that in dimension at least four a Landsberg semi-C-reducible space is a Berwald space. I then examine in some detail the argument that shows that a Minkowski norm of $(\alpha,\beta)$ type is semi-C-reducible, and discuss the conditions for a Finsler space of $(\alpha,\beta)$ type to be a Berwald space in the light of that result.