After considering a more or less random number (i.e., an anchor), people’s subsequent estimates are biased towards that number. Such anchoring phenomena have been explained via an adjustment process that ends too early. We present a formalized version of the insufficient adjustment model and derive from it that decreasing the time that people have to adjust from anchors draws their estimates closer to the anchors. We could not confirm this time-effect on anchoring in four independent studies (N = 898). Moreover, anchoring effects vanished in the two studies that deviated from classical paradigms by using a visual scale or a two-alternative forced choice paradigm to allow faster responses. Although we propose to discard the current version of the insufficient adjustment model, we believe that adjustment models bear the most potential for the future of anchoring research and make suggestions for what these might look like.