We combine two techniques of set theory relating to minimal degrees of constructibility. Jensen constructed a minimal real which is additionally a $\Pi^1_2$ singleton. Groszek built an initial segment of order type $1 + \alpha^\ast$, for any ordinal $\alpha$. This paper shows how to force a $\Pi^1_2$ singleton such that the $c$-degrees beneath it, all represented by reals, are of type $1 + \alpha^\ast$, for many ordinals $\alpha$. We also examine the definability $\alpha$ needs to be so represented by a real.