If we are talking bucket, I would follow my steps above.
In reality you are taking a bucket that was sanitary for one beer, so it should be sanitary for the other...however, it is not worth the risk to me. Get a paper towel damp with sanitizer and wipe off the krausen ring and wipe down the sides. Then with a spray bottle spray down the sides of the bucket. Run the bucket lid under hot water to remove any deposits and then spray it liberally with sanitizer. Clean and sanitize your airlock.
Probably overkill, but how much time are we talking here? 10 minutes? Worth every bit of it in my brewery.