33a. Between two words, phrases, or subordinate clauses
33aDo not use a comma with a coordinating conjunction that joins only two words, phrases, or subordinate clauses.
Though a comma should be used before a coordinating conjunction joining independent clauses (see 32a) or with a series of three or more elements (see 32c), these rules should not be extended to other compound word groups.
The coordinating conjunction and links two verbs in a compound predicate: discovered and came.
The coordinating conjunction but links two subordinate clauses, each beginning with that.