This is an issue that is VERY misunderstood. I am copying here the section from my book, beginning on page 401 in the chapter on "Where NOT to Put Punctuation." Normally, I do not copy an entire section, but this one bears reading in its entirety.
27.9: No Punctuation: In Compound Dependent Construction
Definition
Compound Construction: Compound construction is two or more grammatical elements -- words, phrases, or clauses -- that are joined by a coordinate conjunction: and, but, or, nor, and sometimes the word for.
She had searched the house but not the garage.
I did not know where to go or what to do.
I called because I hadn’t heard from her and because I was worried.
Definition
Dependent Clause: A dependent clause is a group of related words that has a subject and verb; that does not stand alone to express a complete thought because it has an introductory word (a relative pronoun or a subordinate conjunction), which is part of the dependent clause; and that, as a unit, has a function in the sentence.
I don’t know (whether he will be waiting).
The doctor (whom I called) was able to prescribe it.
(While he was sleeping), someone broke into the house.
I am asking (whether you were able to clearly see the door of the liquor store).
There are several here (that seem to fit the bill).
(Because he had had a prior accident), there were insurance questions.
See Chapters 5 and 6 for a discussion of dependent clauses.
RULE:
No Punctuation.9: Do not put a single separating comma in compound dependent construction, that is, when a coordinate conjunction joins elements that cannot stand alone to express a complete thought.
- Joining verbs = no comma
- Joining completer words = no comma
- Joining two prepositional phrases = no comma
- Joining dependent clauses = no comma