That pesky comma before the conjunction linking independent clauses

From today's News Sentinel:

"The new head of the University of Tennessee’s main campus in Knoxville aims to minimize the harm of imminent state budget cuts with careful planning but he said effects will be felt at the classroom level."

Whoops! The prolific and talented Chloe White forgot the comma before the "but."

Harbrace 12a A comma ordinarily precedes a coordinating conjunction that links independent clauses.

as in --

INDEPENDENT CLAUSE, . . {and but or for} . . INDEPENDENT CLAUSE,
subject + predicate, . . . . {not so yet} . . subject + predicate

The minutes would pass, and then suddenly Einstein would stop pacing as his face relaxed into a gentle smile.

BUT

13b Delete commas that immediately precede or follow coordinating conjunctions unless they link independent clauses.

as in (remove the parenthesized comma)

I fed the dog (,) and put it out for the night.

In other words, if there's just one subject and two predicates, no comma.