With the fast increase in Web activities, Web data mining has recently become an important research topic and is receiving a significant amount of interest from both academic and industrial environments. While existing methods are efficient for the mining of frequent path traversal patterns from the access information contained in a log file, these approaches are likely to over evaluate associations. Explicitly, most previous studies of mining path traversal patterns are based on the model of a uniform support threshold, where a single support threshold is used to determine frequent traversal patterns without taking into consideration such important factors as the length of a pattern, the positions of Web pages, and the importance of a particular pattern, etc. As a result, a low support threshold will lead to lots of uninteresting patterns derived whereas a high support threshold may cause some interesting patterns with lower supports to be ignored. In view of this, this paper broadens the horizon of frequent path traversal pattern mining by introducing a flexible model of mining Web traversal patterns with dynamic thresholds. Specifically, we study and apply the Markov chain model to provide the determination of support threshold of Web documents; and further, by properly employing some effective techniques devised for joining reference sequences, the proposed algorithm dynamic threshold miner (DTM) not only possesses the capability of mining with dynamic thresholds, but also significantly improves the execution efficiency as well as contributes to the incremental mining of Web traversal patterns. Performance of algorithm DTM and the extension of existing methods is comparatively analyzed with synthetic and real Web logs. It is shown that the option of algorithm DTM is very advantageous in reducing the number of unnecessary rules produced and leads to prominent performance improvement.