You have just finished serving nine years in prison on a child-pornography conviction when the probation office petitions the court to add a condition of release obligating you to successfully complete a sex-offender treatment program. This program, in turn, obligates you to complete a "non-deceptive sexual history polygraph," and to agree that the examiner will report any crimes you confess to authorities.
This smells like a Fifth Amendment violation, so you object to the condition. The district court agrees! Victory! The court modifies the treatment condition to exclude any confession requirement (except as to your offense of conviction).
A few months later, your treatment provider says court order? What court order? And tells you that you have to answer the following polygraph questions or leave the program:
2. Have you had sexual contact with a family member or relative? If yes, how many times?
3. Have you ever physically forced or threatened anyone to engage in sexual contact with you? If yes, how many times?
4. Have you ever had sexual contact with someone who was physically asleep or unconscious? If yes, how many times?
Surely the district court will protect you, having previously prohibited such questions? Alas, no. The district court reconsiders its earlier order and finds no real risk of incrimination. The court orders you to take the polygraph. The date is January 27. The polygraph is scheduled for February 11.
You file a notice of appeal and ask for a stay of the court's order. The government responds that it will seek your remand to prison if you do not take the polygraph.
The district court denies the stay on February 10. The exam is less than a day away. You seek an emergency stay from the Tenth Circuit, filing your request just before midnight.
Exam day arrives. Fearing an arrest should you not comply, you drive to the examiner's office. You are in the parking lot when you hear the sound of pounding hooves. Two men on white horses gallop around the corner. It's Tenth Circuit Judges Gorsuch and Matheson! They have stayed the polygraph order just in time!
Your appeal from the district court's polygraph order proceeds apace, and at last you are vindicated---the Tenth Circuit holds that the polygraph would be testimonial, incriminating, and compelled, and therefore the court order to take it violated the Fifth Amendment.
Lots of good stuff here on both what counts as an authentic danger of self-incrimination ("The district court mistakenly assumed that an assurance from the government was a substitute for immunity."), and what counts as compulsion ("A witness is compelled under the Fifth Amendment as soon as the government threatens him with a substantial penalty."). Want to know more? Read United States v. Von Behren.