The current document is directed to methods and systems for testing web sites. In certain implementations of the methods and systems, a testing service collects customer page-access and conversion information on behalf of a web site. The testing service is straightforwardly accessed and configured, through a web-site-based user interface, and is virtually incorporated into the web site by simple HTML-file modifications. A more efficient web-site-testing system nonuniformly distributes web-site accesses among web-page variants in order to more quickly and computationally efficiently determine a most effective web-page variant among a set of tested web-page variants. In certain implementations, nonuniform distribution of web-site accesses among web-page variants is facilitated by a Bayesian-inference method.