When a linear order has an increasing surjection onto each of its suborders we say that it is strongly surjective. We prove that countable strongly surjective orders are the union of an analytic and a coanalytic set, and that moreover they are complete for this class of sets. If time allows it, I'll also discuss the existence of uncountable strongly surjective orders. This is a joint work with Riccardo Camerlo and Alberto Marcone.