Abstract: An acceptor for money items such as coins or banknotes produces a money item parameter signal (x1) depending on a sensed characteristic of the money item. A store (12) provides window data corresponding to normal acceptance ranges of values of the parameter signal for a money item of a particular denomination (NAW), as well as restricted acceptance windows (RAW). A processor (11) determines when an occurrence of the parameter signal (x1) may represent a fraudulent money item and then for subsequent sensed money items compares the value of the parameter signals (x1) with the restricted acceptance range (RAW). The RAW range is used until n successive true coins are inserted or a time t has lapsed. After a fraudulent attempt, the values of n and t are increased so that a fraudster cannot then insert n true coins or wait a time t and attempt another fraudulent coin insertion. Also, a focused rejection window (FRW) rejects coins with suspiciously close parameter signals, which could form part of a counterfeit set.