On-line algorithms are essential for service providers to quickly set up bandwidth-guaranteed paths in their backbone or transport networks. A minimum-interference routing algorithm uses the information regarding the ingress-egress node pairs for selecting a path in the case of on-line connection requests. According to the notion of minimum interference, the path selected should have a minimum interference with paths considered to be critical for satisfying future requests. Here we introduce a new class of minimum-interference routing algorithms, called "simple minimum-interference routing algorithms" (SMIRA), that employ an efficient procedure. These algorithms use static network information comprising the topology and the information about ingress-egress node pairs, as well as the link residual bandwidth. Two typical algorithms belonging to this class are introduced, and their performance is evaluated by means of simulation. The numerical results obtained illustrate their efficiency, expressed in terms of throughput, and fairness.