Criterial Freezing is a particular instance of freezing arising in criterial configurations, i.e., in configurations dedicated to the expression of scope-discourse properties. Recent proposals (e.g., Rizzi 2015a,b) try to deduce criterial freezing effects from more elementary ingredients of linguistic computations, most notably from the labeling algorithm proposed in Chomsky (2013). In this paper, we explore the consequences of this approach for the syntax of small clauses. This leads us to work out a cartography of small clauses, both in selected domains (as in English and Romance), and as main clauses (as in Hebrew, following Shlonsky2000). The cartography involves distinct subject positions in the structure of the IP, which are associated with distinct interpretive properties at the interface. Special attention is devoted to the syntax of small clauses with a non-verbal, pronominal copula in Hebrew. Direct and inverse copular sentences are analyzed according to the proposed structural map, and various freezing effects are traced back to the theoretical ingredients introduced at the outset.