The magnetohydrodynamic slip flow of an electrically conducting, non-Newtonian fluid past a shrinking sheet is of concern of the present paper. The physical pure exponential type solutions are targeted to investigate whether they are unique or multiple under the influence of slip flow conditions. The physical parameters are, respectively, viscoelasticity (non-Newtonian), magnetic parameter, mass suction parameter and slip parameter. A theoretical analysis is implemented to explore the domains of existence or nonexistence as well as unique or multiple slip flow solutions. It is shown that the shrinking sheet MHD slip flow of non-Newtonian fluid in the limit of no-slip coincides with the recently studied one by the present author. Full analytical structure is also possible in the large asymptotic slip limit. The presence of a magnetic field has also substantial effects on velocity and temperature fields. (C) 2012 Elsevier Ltd. All rights reserved.