This paper presents a computational study that explores the design of rigid steel frames by considering construction related costs. More specifically, two different aspects are investigated in this study focusing on the effects of (a) reducing the number of labor intensive rigid connections within a frame of given geometric layout, and (b) reducing the number of different member section types used in the frame. A genetic algorithm based optimization framework searches design space for these objectives. Unlike some studies that express connection cost as a factor of the entire frame weight, here connections and their associated cost factors are explicitly represented at the member level to evaluate the cost of connections associated with each beam. In addition, because variety in member section types can drive up construction related costs, its effects are evaluated implicitly by generating curves that show the trade off between cost and different numbers of section types used within the frame. Our results show that designs in which all connections are considered to be rigid can be excessively conservative: rigid connections can often be eliminated without any appreciable increase in frame weight, resulting in a reduction in overall cost. Eliminating additional rigid connections leads to further reductions in cost, even as frame weight increases, up to a certain point. These complex relationships between overall cost, rigid connections, and member section types are presented for a representative five-story steel frame.