It is essential that rotating engines are assembled so that they are straight (straight-build) to satisfy the vibration and functional requirements of the engine. Geometric variations in different components can have a significant impact on the straight-build of an assembly. This paper considers the use of optimization methods to take account of these geometric variations. Five assembly-optimization methods for the straight build of an assembly are investigated with the aid of a connective assembly model that calculates the variation propagation in the assembly. The optimization methods used are; (i) minimizing the distances from component centres to table axis; (ii) minimizing the distance between actual and nominal component centres; (iii) minimizing the angular errors between actual and nominal planes; (iv) target-axis build assembly optimization; (v) changing-axis-build assembly optimization. Two 2D case-studies are investigated to analyse the suitability of the different optimization procedures. Simulation results show that optimization Procedures 1 and 3 have great potential to be applied to real assemblies.