Within the framework of the European Fusion Programme (EFDA) a design activity has been started in late 2004 by the EFDA Close Support Unit at Garching (FRG) to design a 12.5 T superconducting dipole magnet. The final goal of this activity is to define a "minimum cost" and "minimum risk" dipole to be built within the next 3 years by European industries. The newly built magnet shall be hosted in one of the existing cryogenic laboratories in the EU to test, in particular, the full size conductor samples that shall be produced during the ITER magnets procurement. As a result of this study-carried out in cooperation with several European laboratories-different concepts have been analyzed and optimized. All designs are based on the use of high current density Nb3Sn strands (j(c) similar to 2000 A/mm(2) at 12 T/4.2 K). It is assumed that these strands can be cabled either as Cable In Conduit Conductors (CICC) or as Rutherford-type Cables (RC) and then wound as planar racetrack, non-planar (saddle) or cos theta coils. The aim of this paper is to provide an overview of this study activity with particular emphasis to the optimization steps followed in the design of each magnet concept. Four different types are described: a planar CICC/RC-based coil, a saddle CICC-based coil and a cos theta RC-based coil. Each design is described together with the salient optimization steps that include electromagnetic, structure mechanic and thermo-hydraulic analyses as well as different manufacturing constraints.