Parentheses are included in their host sentences, but at the same time they show unintegrated behavior. This article studies this Janus-faced phenomenon from a syntactic point of view. There are two main parts. The first introduces the term Invisibility for syntactic independence based on the absence of c-command relations, which is a particular way of defining structural independence. A number of tests indicate that parentheses and other paratactic constituents are indeed invisible, but specific attention is paid to the various difficulties that show up in establishing such a conclusion. The examples are drawn primarily from Dutch and English. The second part develops a structural proposal for parentheses within a Minimalist type of grammar which takes into account their contradictory properties. Parentheses, it is argued, are adverbial phrases attached by means of a nonsubordinative inclusion relation that can be used in other paratactic configurations as well, in particular appositional constructions.