In this Research Full Paper we explore the factors that traditionally minoritized students consider when selecting a graduate school to pursue a doctoral degree in an engineering discipline. To this end, we used case study methods to analyze the experiences of ten traditionally minoritized students through interviews conducted immediately after they had selected their graduate programs, but before they had commenced their studies. Our findings show that in choosing an institution, the most salient ideals these students hold are related to the offer of funding towards their degree and an alignment with their initial research interests. However, they described having made compromises on ideals related to their personal experience and racial identity, the most prominent being finding a faculty mentor with a similar racial background, finding a racially diverse institution, or being located in a geographical location they perceived to be more amenable to their individual identities. These findings suggest that continuing to increase the recruitment of traditionally minoritized faculty in engineering schools would have a direct impact on minoritized student recruitment, by thus helping to create spaces where more of their racial identity ideals are met and fewer compromises are made. Equally important to the recruitment of traditionally minoritized students is the transparency of funding opportunities during the recruitment and application processes, and the publication of current research opportunities within the institution.