Judge Posner elaborates on "Privacy" in Northwestern Memorial Hospital v. Ashcroft, and Professor Dorf explains.
The case rules on whether the Attorney General may get medical records of some 45 patients in connection to defending the Partial Birth Abortion Ban Act. Ashcroft wanted the records to defend the Congressional findings that "partial-birth abortion is never necessary to preserve the health of a woman, poses significant health risks to a woman upon whom the procedure is performed, and is outside of the standard of medical care."
Ashcroft contended that because he sought the records without patient identification, privacy concerns were not implicated. That was the question in front of Posner.
Here's Dorf:

It grounded its judgment in Federal Rule of Civil Procedure 45(c)(A)(iv), which authorizes judges to quash any subpoena that "subjects a person to undue burden."
...
To determine whether the subpoena imposed an undue burden, the court weighed the burden of compliance against the utility of the information sought.
[explains one alternative for finding a burden]
Nonetheless, Judge Posner pointed to another sort of burden that is not so readily dismissed. He explained that the 45 patients will have their privacy violated--even if their identities would not be revealed.
He provided the following analogy: "Imagine if nude pictures of a woman, uploaded to the Internet without her consent though without identifying her by name, were downloaded in a foreign country by people who will never meet her. She would still feel that her privacy had been invaded." Patients whose redacted late-term abortion records were produced in discovery, Posner suggested, would feel violated in the same way.

I'm always interested in finding out what, exactly, the privacy interest is. While it certainly isn't an enumerated right, I'm inclined to believe it exists, in some capacity- if nothing else, via the 9th amendment. I read a neat chapter in Professor Orth's Due Process of Law primer- and might throw in a post on his explanation of substantive due process.
In any event, the use of Posner's opinion might be interesting to watch.