The piezoelec. switching of antiferroelec. domains by the simultaneous application of an elec. field Ei and mechanical stress T jkis proposed as a direct method for examg. whether some spinel compns. do have point symmetry 43m and concomitant antiferroelec. ordering as proposed by Grimes. For piezoelec. antiferroelecs., the switching energy is Δg = 2dijkEiT jk (dijk = piezoelec. coeff.). For point symmetry 43m, various possible switching procedures have been described in detail. The smallest coercive product of elec. field and stress (E T jk)c is required for switching when the elec. field is chosen along cubic [001], and directional stress along [110] or [110]. For particular directions, for example [111], the colinear application of elec. field and stress also leads to switching. If the assumed prototype with space group F43m (the symmetry proposed by Grimes) is supposed to undergo a phase transition leading to ferrimagnetism, the possible symmetries of the ferrimagnetic domains are given by the magnetic groups I4m'2], Im'm2], and R3m', which are M-maximal subgroups of the prototype magnetic group F43m1]. All 3 ferrimagnetic phases permit piezoelectricity, piezomagnetism, and the linear and 2nd-order magnetoelec. effect. The tetragonal phase (I4m'2]) remains antiferroelec. as the prototype is supposed to be, whereas the orthorhombic (Im'm2]) and trigonal (R3m') phases become ferroelec. The full lattice of subgroups of F43m1] is presented.