Dams and barriers interrupt aquatic connections between tributaries and their endpoints (e.g., lakes). Habitat fragmentation by barriers both hinders and facilitates the conflicting management objectives of restoring native species and controlling invasive species (i.e., connectivity conundrum). Selective connectivity, where taxa and potentially individuals can be discriminated on the basis of management or conservation objectives, presents a potential solution to the connectivity conundrum. Historically, efforts to combine fish passage and invasive species control needs have focused on designs targeting a single factor or trait (e.g., leaping ability) to pass desirable and block invasive fishes. Efficacy of these single-factor designs has been mixed, but limited, depending on species, location, and trait targeted. To achieve selective fish passage, tools that build on insights from past successes and failures involving both traditional fish passage science and invasive species management techniques must be integrated and the physical and biological attributes, including behaviours, of target fishes must drive fishway design. The problem of selective fish passage is essentially a problem of sorting an assortment of things. We seek an eco-engineering approach inspired by single-stream recycling, which evolved over the past 25yrs through advances in automation and integration of multiple technologies to separate mixed materials. Using the context of invasive sea lamprey control in the Great Lakes Basin, we outline a conceptual framework of selective connectivity for fish passage while discussing potential obstacles, realistic expectations, and implications to ecosystem restoration.