Over the past decades, the concept of "high entropy alloys" has become a source of inspiration for the field of metallurgy as we try to identify yet to be explored regions in the metal alloy space with properties that can potentially surpass those of alloys currently in use in a number of applications. The "high entropy" premise of much of the HEA program in the early years has given way to the argument that the HEA space is vast and therefore there are boundless opportunities for further discovery. While strictly speaking the HEA alloy+process space indeed is infinite, in this work we present some recent investigations that suggest that, while big, the feasible HEA space in any given sub-sector (e.g. FCC HEAs, RHEAs, etc) is severely constrained by typical alloy design considerations. Combining CALPHAD, physics-based models, machine learning, search/optimization algorithms we present a more nuanced view of the HEA space.