Judicial Improvement and Integrity Act of 2001 - Amends the Federal criminal code to expand the scope of provisions concerning, and increase penalties for, tampering with witnesses, victims, or informants. Sets forth provisions prohibiting the use of (or threat to use) physical force with intent to influence, delay, or prevent the testimony of any person in an official proceeding. Specifies that whoever conspires to tamper with a witness, victim, or informant, or to retaliate against any such individuals, shall be subject to the same penalties as those prescribed for the offense the commission of which was the object of the conspiracy.

Modifies various code prohibitions to permit imposition of both a fine and imprisonment, instead of just one or the other, including for contempt and for destruction of letter boxes or mail.

Directs that any counts of an indictment or information that are dismissed pursuant to a plea agreement be reinstated by the District Court if: (1) such counts were originally filed within the applicable limitations period; (2) the counts were dismissed pursuant to a plea agreement approved by the District Court under which the defendant pled guilty to other charges; (3) the guilty plea was subsequently vacated on the motion of the defendant; and (4) the United States moves to reinstate the dismissed counts within 60 days of the date on which the order vacating the plea becomes final.