This work proposes the use of an alternative error representation for Goal-Oriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation of the error of an alternative dual problem. From the new representation, we derive element-wise estimators to drive the adaptive algorithm. The method is applied to a one dimensional (1D) steady state convection dominated diffusion problem with homogeneous Dirichlet boundary conditions. This problem exhibits a boundary layer that produces a loss of numerical stability. The new error representation delivers sharper error bounds. When applied to a p-GOA Finite Element Method (FEM), the alternative error representation captures earlier the boundary layer, despite the existing spurious numerical oscillations. (C) 2017 The Authors. Published by Elsevier B.V. V. Darrigrand, A. Rodriguez-Rozas and D. Pardo were partially funded by the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2013-40824-P, MTM2016-76329-R, MTM2016-81697-ERC and the Basque Government Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)". A. Rodriguez-Rozas and D. Pardo were also partially funded by the BCAM "Severo Ochoa" accreditation of excellence SEV-2013-0323 and the Basque Government through the BERC 2014-2017 program. A. RodrIguez-Rozas acknowledges support from Spanish Ministry under Grant No. FPDI- 2013-17098. D. Pardo was also partially funded by the ICERMAR Project KK-2015/0000097. I. Muga was partially funded by the CYTED 2011 project 712RT0449 and the FONDECYT project 1160774. All authors were also partially funded by the European Union's Horizon 2020, research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644202. All Authors have received funding from the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU)