Off-the-cuff

He made a splendid off-the-cuff speech.

The president's off-the-cuff remarks have gotten him into hot water.

Even his everyday speech was an off-the-cuff, tangential, disjointed narrative.

Did you make your speech off-the-cuff?

He made a few off-the-cuff remarks before launching into his prepared speech.

Off-the-Cuff Obama Line Put U.S. in Bind on Syria [title]

Trump’s Off-the-Cuff Tweets Strain Foreign Ties [title]

Even when people are trying to sell you something, their messages seem off-the-cuff, like trustworthy recommendations rather than sponsored shilling.