In this talk, we study, for a given first-order theory \(T\), which countable models of \(T\) can be presented effectively. We consider this question for a particular class of theories, the so-called strongly minimal disintegrated theories, where the countable models can be characterized by their dimension. The spectrum of computable models of \(T\) is the subset \(S\) of \(\omega+1\) such that \(\alpha\) is in \(S\) if and only if the \(\alpha\)-th model of \(T\) can be effectively presented. We examine the class of strongly minimal disintegrated theories in computable relational languages where each relation symbol defines a set of Morley rank at most 1. We characterize the spectra of computable models of such theories (exactly, with the exception of three sets) under the assumption of bounded arity on the language, and (with the exception of three sets and one specific class of sets) without that assumption. We also determine the exactly seven possible spectra for strongly minimal theories in binary relational languages and show that there are at least nine but no more than eighteen spectra of disintegrated theories in ternary relational languages.