A model with Suslin trees but no minimal uncountable linear orders other than ω1 and −ω1

We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than ω 1 and − ω 1 , answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that one can force CH together with a restricted form of ladder system uniformization on trees, all while preserving a rigid Suslin tree.