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In the Simply Typed λ-calculus Statman investigates the reducibility relation ≤βη between types: for A,B∈T0, types freely generated using → and a single ground type 0, define A≤βηB if there exists a λ-definable injection from the closed terms of type A into those of type B. Unexpectedly, the induced partial order is the (linear) well-ordering (of order type) ω+4. In the proof a finer relation ≤h is used, where the above injection is required to be a Böhm transformation, and an (a posteriori) coarser relation ≤h+, requiring a finite family of Böhm transformations that is jointly injective. We present this result in a self-contained, syntactic, constructive and simplified manner. En route similar results for ≤h (order type ω+5) and ≤h+ (order type 8) are obtained. Five of the equivalence classes of ≤h+ correspond to canonical term models of Statman, one to the trivial term model collapsing all elements of the same type, and one does not even form a model by the lack of closed terms of many types.