We determine the structure of the set of intermediate β \beta -shifts of finite-type. Specifically, we show that this set is dense in the parameter space Δ ≔ { ( β , α ) ∈ R 2 : β ∈ ( 1 , 2 ) and 0 ≤ α ≤ 2 − β } . \begin{align*} \Delta \coloneq \{ (\beta , \alpha ) \in \mathbb {R}^{2} \colon \beta \in (1, 2) \; \text {and} \; 0 \leq \alpha \leq 2 - \beta \}. \end{align*} This generalises the classical result of Parry from 1960 for greedy β \beta -shifts.