In The Search For Spock Scotty rigs the Enterprise-A to run primarily on automation with only a bridge crew (although this does fail when they engage in combat.)
Scotty: "Admiral, I set up the Enterprise-A for full automation. She'll give us no trouble on our trip to the Genesis Planet."
Kirk: "Good work, Scotty, but we're going to be taking the original Enterprise instead, on account of the Enterprise-A not being built yet."
Scotty: "What? Where in blazes was I all afternoon?"