setoff

1. Something, such as a decoration, that sets off something else by contrast.
2. Something that offsets or compensates for something else; a counterbalance.
3. 1. A counterclaim.
   2. Settlement of a debt by a debtor's establishing such a claim against a creditor.
4. Architecture. A flat projection, as from a wall; a ledge.
5. Printing. See offset (sense ).

In general: counterclaim by Defendant against Plaintiff that grows from an independent Cause of Action and diminishes the plaintiff's potential recovery; a counterdemand arising out of a transaction different from that on which the plaintiff's cause of action is based. It does not deny the justice of the plaintiff's claim but seeks to balance it in whole or in part by a counterobligation alleged to be due by the plaintiff to the defendant in another transaction.

Tax law: the amount of refund that a taxpayer could claim to be offset against the amount of deficiency that could be properly assessed; conversely, the amount of deficiency the government could assess can be offset by the amount the taxpayer could properly claim as a refund for the same taxable year.

noun

Something to make up for loss or damage: amends, compensation, indemnification, indemnity, offset, quittance, recompense, redress, reimbursement, remuneration, reparation, repayment, requital, restitution, satisfaction. See substitute.

The noun has one meaning:

Meaning #1: structure where a wall or building narrows abruptly
  Synonyms: set back, offset