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Purpose Aerodynamic shape optimisation is complex because of the high dimensionality of the problem, the associated non-linearity and its large computational cost. These three aspects have an impact on the overall time of the design process. To overcome these challenges, this paper aims to develop a method for transonic aerodynamic design with dimensionality reduction and multifidelity techniques. Design/methodology/approach The developed methodology is used for the optimisation of an installed civil ultra-high bypass ratio aero-engine nacelle. As such, the effects of airframe-engine integration are considered during the optimisation routine. The active subspace method is applied to reduce the dimensionality of the problem from 32 to 2 design variables with a database compiled with Euler computational fluid dynamics (CFD) calculations. In the reduced dimensional space, a co-Kriging model is built to combine Euler lower-fidelity and Reynolds-averaged Navier stokes higher-fidelity CFD evaluations. Findings Relative to a baseline aero-engine nacelle derived from an isolated optimisation process, the proposed method yielded a non-axisymmetric nacelle configuration with an increment in net vehicle force of 0.65% of the nominal standard net thrust. Originality/value This work investigates the viability of CFD optimisation through a combination of dimensionality reduction and multifidelity method and demonstrates that the developed methodology enables the optimisation of complex aerodynamic problems.