Is there an English equivalent to "get rid of the goat"?

Danny was living in a small house with five other people, and the stress was getting to him. He went to the town elder to ask for advice.

"Buy a goat", said the town elder, "and let it live in your apartment. If that doesn't help, come see me again in a month."

A month later, Danny came back and said "now I've got six people and a goat in my tiny apartment, and I'm more stressed than ever before!"

"Get rid of the goat", said the town elder.

And Danny was no longer stressed.

The phrase "getting rid of the goat" is quite common in Israel (להיפטר מן העז in Hebrew) to mean returning to a lower level of stress from a higher level, and thereby feeling less stressed by comparison. Is there a similar saying or tale in American English?

As a US-based software developer, I have heard a similar story. I'm not sure if it's well-known enough to be used as an idiom, but it at least shows the pervasiveness of that form of joke or story.

This started as a piece of Interplay [a video game publisher] corporate lore. It was well known that producers (a game industry position, roughly equivalent to PMs [project managers]) had to make a change to everything that was done. The assumption was that subconsciously they felt that if they didn't, they weren't adding value.

The artist working on the queen animations for Battle Chess was aware of this tendency, and came up with an innovative solution. He did the animations for the queen the way that he felt would be best, with one addition: he gave the queen a pet duck. He animated this duck through all of the queen's animations, had it flapping around the corners. He also took great care to make sure that it never overlapped the "actual" animation.

Eventually, it came time for the producer to review the animation set for the queen. The producer sat down and watched all of the animations. When they were done, he turned to the artist and said, "that looks great. Just one thing - get rid of the duck."

(Folk tale, as reported in a post from Coding Horror by Jeff Atwood)

So, at least for software developers, get rid of the duck is an equivalent saying.

Is there a similar saying or tale in American English?

I don't know of an equivalent for the short form, but since you also ask for a similar tale, perhaps the old joke:

Q: Why do you keep banging your head against that wall/hitting yourself with a hammer/whipping yourself etc.?

A: Because it feels so good when I stop.

I'm not sure of the origin of the joke, but it's well-known enough that the second line can be used stand-alone, as with this book title, the title of this blog post about petty online registration frustrations, this chapter from the book Bodybuilding Motivation, etc.

However, for full effect you might need the full story, which also pops up in such widely divergent places as a New York Times Op Ed piece, a column with advice for pastors, a motivational blog, and a popular Grey's Anatomy quote.

Note that an abbreviated version, quit banging your head against the wall, is idiomatic with a slightly different meaning, more like "what you're doing is futile, so stop wasting your time." See Dictionary.com.

The town elder is helping Danny to put things in perspective, to understand that matters can always be worse. He is also teaching Danny that you don't know how good you have it until it's gone, i.e., to learn to appreciate what you have, to focus on the positive.

There's a bit of a double entendre in you don't know how good you had it until it's gone. First, Danny quickly understood that the initial arrangement he had was far preferable to that with the goat -- try living with a goat! Second, Danny appreciated that fact doubly when the goat was gone.