In the following sentence, the secondary clause isn’t truly independent; it lacks a subject, yet it conveys an almost-complete thought: “I left Susan a message last week but haven’t heard back from her yet.” My question is whether a comma precedes but even though a subject doesn’t follow but. Put another way, is the secondary clause’s implied subject, I¸ sufficient to require a comma before the coordinating conjunction?There is no “implied” subject in the sentence “I left Susan a message last week but haven’t heard back from her yet.” The sentence’s stated subject is I. It’s the subject of both verbs, the one before and the one after the but. The answer, therefore, is that no comma is needed before the but.
The rule for but is the same as that for the other six coordinating conjunctions: and, for, or, nor, so, and yet.
If the conjunction precedes an independent (main) clause, use a comma: “Jack tried a new diet, but he still gained weight.”
If the but is not followed by an independent clause, no comma is needed: “Jack tried a new diet but still gained weight.”
If a writer finds himself hesitating over a sentence like the one in the example, the easiest way to settle the comma question is to supply another subject for the second verb: “I left Susan a message last week, but I haven’t heard back from her yet.”
Source: Daily Writing Tips