Pushing myself on the harder writing again today...
In 1988, the feature that [N. T.] Wright found common to this third quest [for the historical Jesus] was a focus on history.  We have to place his sense of this common ground against the backdrop of the era of Barth and Bultmann, when history was de-emphasized in deference to theology  and against the so called "New Quest" in which the criterion of dissimilarity reigned supreme. The criterion of dissimilarity looked for sayings of Jesus that neither fit well within the Jewish context of Palestine nor a later context of Christian faith. Such sayings would surely derive authentically from Jesus, since no one would be motivated to make such a saying up or misdirect an existing one. While this reasoning is sound, the collection of such sayings surely would not give us a picture of Jesus that is anything like he likely was. 
Wright himself would later argue for a criterion of "double similarity."  That is to say, we would expect to find both authentic sayings and events in the life of Jesus somewhere on a trajectory from Jesus' Jewish context to the faith of the earliest church that issued from his life. While Wright thus emphasized the return to history in his initial analysis of the resurgence of Jesus research at the time, that surge would include significant attention to Jesus against the backdrop of his Jewish context, as the title of Vermes' book indicates.  A. E. Harvey, another "quester" that Wright featured, wrote of the "constraints" of history, namely, that for Jesus to communicate to his audiences, "he had to speak a language they could understand, perform actions they would find intelligible, and conduct his life and undergo his death in a manner of which they could make some sense." 
James Dunn in fact considers the work of Sanders a more appropriate place to begin speaking of a third quest for the historical Jesus. "If traditional New Testament scholarship had misrepresented the Judaism with which Paul had to do, how much more was it necessary for Jesus' relationship to his ancestral Judaism to be reassessed.  In this regard, it is not surprising to find that Sanders himself wrote an analysis of the historical Jesus in the decade after his book on Paul, nor to find that Wright includes his work among those of the third quest. ...
 He says of Geza Vermes writing as a historian: "that is the major distinguishing mark of all the 'Third Quest' authors" (Interpretation, 381).
 A situation in which we more or less find ourselves again at the beginning of the twenty-first century.
 For a critique of the criterion of dissimilarity, see "Saving the Quest from the Criterion of Dissimilarity: History and Plausibility," in Jesus, Criteria, and the Demise of Authenticity, Chris Keith and Anthony Le Donne, eds. (London: T & T Clark, 2012), 115-31.
 Jesus and the Victory of God (Minneapolis: Fortress, 1996) 132.
 In his magnum opus on the historical Jesus, James Dunn highlights the way in which late nineteenth century questers tried to distance Jesus from his Jewishness. Ernst Renan, for example, wrote that, "Fundamentally there was nothing Jewish about Jesus," quoted in Dunn, Jesus Remembered (Grand Rapids: Eerdmans, 2003), 86. Later in that section, Dunn writes, "In the history of Jesus research nothing has evidenced the flight from history more devastatingly than the persistent refusal to give any significance to the Jewishness of Jesus" (88).
 A. E. Harvey, Jesus and the Constraints of History (Louisville: Westminster John Knox, 1982), 7*.
 Jesus Remembered, 89.
 Jesus and Judaism (Philadelphia: Fortress, 1985). Wright's analysis of Sanders in this regard is found in Interpretation, 391-96.