The idea of distributing static probe cross-sectional areas so as to render the probe insensitive to Mach number is combined here with that of using non-circular cross-sections to render probes insensitive to yaw and angle of attack. Appropriate non-circular cross-sections are described in detail, and a general means of designing blunt or slender probes to have zero sensitivity to yaw and angle of attack in potential flow is described. Four experimental probes have been tested, and test results are presented. These results show that the probes are quite insensitive to yaw and angle of attack within certain limiting angles, which are assumed to correspond to the onset of flow separation.