recoupment:
n. (17c)

1. The getting back or regaining of something, especially expenses.

2. The withholding, for equitable reasons, of all or part of something that is due.

3. Reduction of a plaintiff’s damages because of a demand by the defendant arising out of the same transaction.

4. The right of a defendant to have the plaintiff’s claim reduced or eliminated because of the plaintiff’s breach of contract or duty in the same transaction.

5. An affirmative defense alleging such a breach.

6. Archaic. A counterclaim arising out of the same transaction or occurrence as the one on which the original action is based.  *  In modern practice, the recoupment has been replaced by the compulsory counterclaim. — recoup, vb. [1]

1. Literally, a cutting back.  Davenport v Hubbard, 46 Vt 200.

A deduction out of the same transaction are allowed to compensate one another, the balance only to be recovered.  National Cash Register Co. v Joseph, 290 NY 200, 86 NE2d 561, 12 ALR2d 812.

The right of a defendant, in the same action, to cut down the plaintiff’s demand either because the plaintiff has not complied with some cross obligation of the contract on which he sues or because he has violated some duty which the law imposes on him in the making or performance of that contract.  20 Am J2d Countcl § 1.
     Recoupment, as distinguished from the offsetting of one transaction against another, means a deduction from a money claim whereby cross demands arising out of the same transaction are allowed to compensate one another and the balance only to be recovered.  National Cash Register Co. v Joseph, 290 NY 200, 86 NE2d 561, 12 ALR2d 812. [2]

1.In pleading, a reduction of a plaintiff’s money claim as a result of a claim of the defendant arising out of the same transaction.  More specifically, the right of a defendant to reduce the plaintiff’s demand because the plaintiff has not fulfilled some obligation of the contract upon which she is suing.  Recoupment is achieved through a counterclaim.  Recoupment should be distinguished from a setoff, which involves cross-demands arising out of different transactions rather than out fo the same transaction.

2. The act of getting back what one has lost. [3]

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