We develop a full-chain tube-based constitutive model [along the lines of Graham et al. J. Rheol. 47, 1171 (2003)] for the nonlinear rheology of bidisperse blends of long and short linear polymers. For a test chain in the blend, we use the physical picture of a fat tube, representing long-lived entanglements with long chains, and a thin tube, representing entanglements with all chains. The model includes the processes of reptation, contour length fluctuation (CLF), constraint release, and stretch relaxation. In the linear rheology regime, we identify a new relaxation process: CLF along the fat tube contour, achieved via a combination of chain motion along the thin tube, and local constraint release of the thin tube as it explores the width of the fat tube. This process is sufficiently fast to relax a significant portion of the long chains before reptation. It provides an explanation of the decrease in terminal time of long chains upon dilution with short chains in a framework where motion along the thin tube is the dominant reptation mechanism. Once the linear rheology is matched, nonlinear rheology is predicted with no further adjustments to the model. The model compares well against several experimental datasets on bidisperse blends. In particular, it predicts the onset rate of extension hardening, which is often significantly below the inverse Rouse time of the long chains. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4707948]