In real-time ultrasonic 3-D imaging, in addition to difficulties in fabricating and interconnecting 2-D transducer arrays with hundreds of elements, there are also challenges in acquiring and processing data from a large number of ultrasound channels. The coarray (spatial convolution of the transmit and receive arrays) can be used to find efficient array designs that capture all of the spatial frequency content (a transmit-receive element combination corresponds to a spatial frequency) with a reduced number of active channels and firing events. Eliminating the redundancies in the transmit-receive element combinations and firing events reduces the overall system complexity and improves the frame rate. Here we explore four reduced redundancy 2-D array configurations for miniature 3-D ultrasonic imaging systems. Our approach is based on 1) coarray design with reduced redundancy using different subsets of linear arrays constituting the 2-D transducer array, and 2) 3-D scanning using fan-beams (narrow in one dimension and broad in the other dimension) generated by the transmit linear arrays. We form the overall array response through coherent summation of the individual responses of each transmit-receive array pairs. We present theoretical and simulated point spread functions of the array configurations along with quantitative comparison in terms of the front-end complexity and image quality.