A lithium ion-conducting compound, having a garnet-like crystal structure, and having the general formula: Lin[A(3-a′-a″)A′(a′)A″(a″)][B(2-b′-b″)B′(b′)B″(b″)][C′(c′)C″(c″)]O12, where A, A′, A″ stand for a dodecahedral position of the crystal structure, where A stands for La, Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and / or Yb, A′ stands for Ca, Sr and / or Ba, A″ stands for Na and / or K, 0<a′<2 and 0<a″<1, where B, B′, B″ stand for an octahedral position of the crystal structure, where B stands for Zr, Hf and / or Sn, B′ stands for Ta, Nb, Sb and / or Bi, B″ stands for at least one element selected from the group including Te, W and Mo, 0<b′<2 and 0<b″<2, where C and C″ stand for a tetrahedral position of the crystal structure, where C stands for Al and Ga, C″ stands for Si and / or Ge, 0<c′<0.5 and 0<c″<0.4, and where n=7+a′+2·a″−b′−2·b″−3·c′−4·c″ and 5.5<n<6.875.