I will describe joint work with Uri Andrews showing that for a strongly minimal theory $T$, if the $\exists_{n+3}$ part of $T$ is $\Delta^0_n$, uniformly in $n$, then all models of $T$ have computable copies. Relativizing this, we obtain the fact that if a strongly minimal theory has a computable model, then all models have $\Delta^0_5$ copies. We hope to replace $\Delta^0_5$ by $\Delta^0_4$. The talk will include background on strongly minimal theories. I hope to say enough about the proof to make clear how it combines serious model theory (Morley rank and degree) with serious computability (constructions by infinitely many workers).