This paper is part of our ongoing research and collaboration on understanding the relations between CAD algorithms, equational constraints and curtains. In our previous work we provided an algorithm that would decompose the hypersurface given by an equational constraint, to produce a sign-invariant quasi-CAD (even in the presence of curtains). That method however fails to take full advantage of multiple equational constraints. Here we provide further clarification to \cite{McCallum2001} and discuss the close relationship between order invariance and lex-least invariance.