We establish a dichotomy theorem characterizing when a treeable Borel equivalence relation E is essentially countable. Under additional assumptions on the treeing, we show that E is essentially countable if and only if there is no continuous embedding of the relation 𝔼₁ into E. In particular, we generalize and provide a classical proof of the analogous result for hypersmooth equivalence relations due to Kechris and Louveau. By considering a special class of treeings, we use our dichotomy to deduce several results about the global structure of the Borel reducibility hierarchy on equivalence relations, namely: the collection of treeable Borel equivalence relations is unbounded in the Borel-reducibility hierarchy; for every Borel equivalence relation which is not essentially hyperfinite we may find equivalence relations of arbitrarily high descriptive complexity with which it is incomparable under Borel reducibility; and for a sufficiently complicated Borel Wadge class Γ there is no minimum non-potentially Γ equivalence relation. This is joint work with Dominique Lecomte and Ben Miller