This work presents an efficient method for assessing mooring system designs for floating wind turbines (FWTs) based on frequency-domain analysis. The method is used to explore the design space and design-driving constraints for catenary and semi-taut mooring systems for semi-submersible FWTs with power ratings from 5 to 25 MW. The proposed method combines a previously presented model for low-frequency rotor-aero-servo dynamics in frequency-domain with a frequency-domain lumped mass model for estimating the wave-frequency dynamic tension, which has often been treated quasi-statically in previous studies. Multiple design constraints including ultimate limit state, fatigue limit state, and maximum allowable offset were considered in design space exploration and optimization. The main design-driving criteria were found to be the maximum offset and fatigue life. The resulting designs were tested using nonlinear coupled time-domain analysis and found to satisfy all the required design criteria. The frequency-domain model captures the main trends of the motion and tension statistics of the FWTs while providing conservative estimates for fatigue damage for most conditions. The discrepancies between the frequency- and time-domain results are mainly due to overestimation of the surge resonance response due to the linearization of aerodynamic damping in the frequency-domain model. • Frequency-domain model with rotor-aero-servo dynamics and mooring line dynamics. • Both low- and wave-frequency tension processes contribute significantly to fatigue. • FWT mooring design is mainly driven by fatigue and maximum offset constraints. • Larger maximum offsets result in significant reduction in FWT mooring material cost. • Chains that satisfy FLS for a 25 MW FWT are larger than current commercial sizes.