After considering a more or less random number (i.e., an anchor), people’s subsequent estimates are biased toward 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, which captures the idea that decreasing the time that people have to adjust from anchors draws their estimates closer to the anchors. In four independent studies (N = 898), we could not confirm this effect of time on anchoring. 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 that the current version of the insufficient adjustment model should be discarded, we believe that adjustment models hold the most potential for the future of anchoring research, and we make suggestions for what these might look like.