To examine the prospect of full closure of relevant material flows, and the policy mix and transition to achieve it, I critically approach the popular notion of a ‘circular economy’ (CE) from six complementary perspectives: (i) lessons from ecosystem recycling, (ii) limits posed by thermodynamics, (iii) material rebound and material-to-energy shifting, (iv) market processes, (v) consumer and firm behaviour, and (vi) geography and transport. The unprecedented ambition of the CE goal requires a permanent incentive structure to assure that all decisions by consumers, producers, investors and innovators are in line with circularity. Rather than hoping to realise this at short notice, policy will likely have to go through subsequent stages of advancement. This is best guided by sub-aims such as balancing ‘local and non-local recycling’ and limiting material rebound and material-to-energy shifting. Due to complicated and inexact compromises between durability, product light-weighting, reparability, decomposability and recyclability, one cannot hope to formulate simple rules for optimal CE policy. In line with this, we should, at best, expect to achieve a ‘semi-circular economy’.