An approach for combining sequentially unreliable sources of evidence is presented in this paper. The sources of evidence are not considered as equi-reliable in the combination process, and no prior knowledge on their reliability is required. The reliability of each source is evaluated on the fly by a distance measure, which characterizes the variation between one source of evidence with respect to the others. If the source is considered as unreliable, then its evidence is discounted before entering in the fusion process. Dempster's rule of combination and its main alternatives including Yager's rule, Dubois and Prade rule, and PCR5 are adapted to work under different conditions. In this paper, we propose to select the most adapted combination rule according to the value of conflicting belief before combining the evidence. The last part of this paper is devoted to a numerical example to illustrate the interest of this approach.