In this paper, we develop an SUPG spectral element scheme suitable for computations of viscoelastic flows at high Deborah numbers. The novelty of the scheme lies in the derivation of the upwinding factors used in the perturbed test tensors of the weak, form of the equations. These factors are related to the Deborah number and to the local mesh spacing and have been derived using the superconsistency ideas of Funaro [SIAM J. Numer. Anal. 30 (1993) 1664-1676; J. Sci. Comp. 12 (1997) 385-394; Comput. Math. Appl. 33 (1997) 95-103]. Results of applying the method to the benchmark problem of flow past a single confined cylinder demonstrate the superior stability and accuracy properties of the new scheme when compared with the SUPG spectral element method used previously by the authors [J. Non-Newtonian Fluid Mech. 95 (2000) 1-33; Comput. Meth. Appl. Mech. Engrg. 190 (2001) 3999-4018]. The new method gives excellent agreement with reference results in the literature.