An ordinal is called bad [1] or non-Gandy[2] if the supremum of order types of $\alpha$-recursive well-orderings is less than the next admissible after $\alpha$. Since the least bad ordinal is quite large (larger than the least $\Pi_1^1$-reflecting ordinal [1]), this behavior appears unexpectedly when working with ordinals in the range of weakened versions of stability. [2] The least bad ordinal coincides with the least $\Sigma^1_1$-reflecting ordinal. [2]
The least bad ordinal is greater than the least ordinal that is $$\Pi^{1,set}_1$$-reflecting on the class of $$\Pi^{1,set}_1$$-reflecting ordinals. (J. P. Aguilera, The Order of Reflection (2019, arxiv preprint). Accessed 7 September 2022.)