Logical minimalism is part of a more general research programme into the foundations of mathematics and logic that was carried out at the beginning of the 20th century. In the 1940s and 1950s, however, this tradition was redefined in the context of ‘computer science’ when computer engineers, logicians and mathematicians re-considered the problem of small(est) and/or simple(st) machines in the context of actual engineering practices. This paper looks into thisearly history of research on small symbolic and physical machines and ties it to this older tradition of logical minimalism. Focus will be on how the transition of symbolic machines into real computers integrates minimalist philosophies as parts of more complex computer design strategies.