Ground interference distortion is present in aircraft flyover noise spectra acquired using microphones mounted on poles, such as the 1.2-m height required for noise certification. This spectral distortion is undesirable and can be avoided by using microphones that are mounted flush with the surface of a large, flat, acoustically hard surface. However, flush mounting is usually not possible. As a practical implementation of a flush installation, Boeing has developed the flush-dish microphone that consists of a dish placed on the ground with its convex side up. The microphone is flush mounted at the center of the dish. Two designs of this concept, circular and exponential flush-dish microphones, are described in this paper. The first design, the circular flush dish, was found to be free from ground interference effects for all incidence angles except for angles within about 15 deg of the overhead position. In this region, it exhibited periodic spectral modulation due to the interaction between direct and edge-diffracted waves. To diminish the edge effect, a new design, the exponential flush dish, was conceived. The edge was shaped to gradually match the impedance between the dish and the ground and to avoid the in-phase addition of edge-diffracted waves. The experimental results showed the exponential dish to be free from edge diffraction and ground interference effects. Furthermore, the response was insensitive to whether the flush dish was mounted on an acoustically hard surface or a typical natural terrain.