An acceptor for money items, comprises sensor circuitry (S1-S4) to provide individual money items signals (Rs) depending on items of money under test, and a processor configuration (11) to develop for each of the money items under test, a transformed money item signal (Tnew) as a function of the value of the money item signal and at least one variable parameter (A) that is a function of a fraud criterion such as history data (AVG Dn & MAX Dn) relating to the values of the money item signals for previously tested money items, to make a comparison of the values of the transformed money item signals (Tnew) with a fixed window limit value (W2, L3) and to accept each money item if it falls within the window limit.