could the defendant then also admit to some additional, only marginally-related crime?
I suppose, but why would he or she?
Or something altogether unrelated?
Again, of course that could happen, but it is not clear what motivation there would be to admit to random crimes unrelated to what the person is being questioned about.
are strict limits on what the immunity would entail communicated prior to any admission of guilt?
Yep. Also, the content of what the defendant (or witness - it's not always a defendant) will say is also communicated prior to any admission.
Prosecutors can grant immunity in exchange for cooperation, or reach a
plea bargain for a reduced sentence. Before that can happen,
prosecutors need to know what the witness will say and how credible
that testimony is. There is nothing worse than making a deal before
knowing what you are getting in return.
In order to make a deal, prosecutors and defense lawyers engage in
what is known as a “proffer” session, in which the witness is
interviewed and the information being offered is gauged for its
usefulness. Once someone talks with the government, however, the Fifth
Amendment privilege is usually lost.
To deal with that issue, the Justice Department usually enters into an
informal letter immunity agreement — sometimes called “Queen for a
Day” immunity after the 1960s television game show. Such immunity is
only good for the particular proffer session and ends as soon as the
two sides are finished.
Under the letter agreement, the witness provides complete information
to the government without waiving the protections of the Fifth
Unlike immunity granted under the federal statute 18 U.S.C. § 6002,
this is a more informal arrangement that is governed by the terms of
the agreement worked out by the parties. Like any contract, it is
subject to negotiation, and the leverage one party has will affect how
much protection is afforded if there is not a resolution.
Prosecutors typically seek to use the statement to develop new leads
and introduce new evidence gathered as a result of the information
provided. This is not permissible when full statutory immunity is
granted to a witness.
Another provision often sought by the government allows prosecutors to
introduce the statements to impeach a defendant if the case proceeds
to trial and the person testifies in a way that is contradicted by the
statements made in the proffer session. This is included as a way to
deter a witness from giving one story when seeking to resolve a case,
and then saying something different at trial to avoid a conviction.
The federal evidence rules usually do not permit the introduction of
statements made during negotiations related to a potential settlement
of a case. The letter immunity is intended to get around that by
having the witness waive the protection so that the statements can be
used at a trial.