We present new constructions of linear orders which are minimal with respect to being non-$\sigma$-scattered. Specifically, we will show that Jensen's $\diamondsuit$ principle implies that there is a minimal Countryman line, answering a question of Baumgartner. We will also construct the first consistent examples of minimal non-$\sigma$-scattered linear ordersof cardinality greater than $\aleph_1$. In fact this can be achieved at any successor cardinal $\kappa^+$,both via forcing constructions and via axiomatic principles which hold in G\"odel's Constructible Universe. These linear orders of cardinality $\kappa^+$ have the property that their square is theunion of $\kappa$-many chains. This is joint work with James Cummings and Todd Eisworth.