Aerofoils operating in a turbulent flow generate broadband noise by scattering vorticity into sound at the leading edge. Previous work has demonstrated the effectiveness by which serrations, or undulations, introduced onto the leading edge, can substantially reduce broadband leading-edge noise. All of this work has focused on sinusoidal (single-wavelength) leading-edge serration profiles. In this paper, a new leading-edge serration geometry is proposed which provides significantly greater noise reductions compared to the maximum noise reductions achievable by single-wavelength serrations of the same amplitude. This is achieved through destructive interference between different parts of the aerofoil leading edge, and therefore involves a fundamentally different noise reduction mechanism from conventional single-wavelength serrations. The new leading-edge serration profiles simply comprise the superposition of two single-wavelength components of different wavelength, amplitude and phase with the objective of forming two roots that are sufficiently close together and separated in the streamwise direction. Compact sources located at these root locations then interfere, leading to less efficient radiation than single-wavelength geometries. A detailed parametric study is performed experimentally to investigate the sensitivity of the noise reductions to the profile geometry. A simple model is proposed to explain the noise reduction mechanism for these double-wavelength serration profiles and shown to be in close agreement with the measured noise reduction spectra. The study is primarily performed on flat plates in an idealized turbulent flow. The paper concludes by introducing the double-wavelength serration on a 10 % thick aerofoil, where near-identical noise reductions are obtained compared to the flat plate.