<p><it>Abstract—</it>Residue number systems provide a good means for extremely long integer arithmetic. Their carry-free operations make parallel implementations feasible. Some applications involving very long integers, such as public key encryption, rely heavily on fast modulo reductions. This paper shows a new combination of residue number systems with efficient modulo reduction methods. Two methods are compared, and the faster one is scrutinized in detail. Both methods have the same order of complexity, $<tmath>O(\log n)</tmath>$, with $<tmath>n</tmath>$ denoting the amount of registers involved.</p><p><it>Index Terms—</it>Computer arithmetic, cryptography, distributed systems, hardware algorithms, long integer arithmetic, modulo reduction, parallel algorithms, residue number systems.</p>