The title compounds were prepared from the elements by reactions in water-cooled glassy carbon crucibles under an argon atmosphere in a high-frequency furnace. CaPdIn4 crystallizes with the YNiAl4-type structure: Cmcm, a=446.7(3), b=1665(1), c=754.3(5) pm, wR2=0.0465 with 646 F2 values and 24 variables. The structure is built up from a complex three-dimensional [PdIn4] polyanion in which the calcium atoms occupy distorted pentagonal tubes formed by indium and palladium atoms. CaRhIn4 and CaIrIn4 adopt the LaCoAl4-type structure: Pmma, a=867.6(1), b=422.91(8), c=745.2(1) pm, wR2=0.0583 with 468 F2 values and 24 variables for CaRhIn4; a=869.5(1), b=424.11(6), c=746.4(1) pm, wR2= 0.0614 471 F2 values with 24 variables for CaIrIn4. This structure type, too, has a three-dimensional [RhIn4] polyanion which is related to the structure of binary RhIn3. The calcium atoms fill distorted pentagonal prismatic channels formed by indium atoms. Semi-empirical band structure calculations for Ca-RhIn4 and CaPdIn4 reveal strongly bonding In-In, Rh-In and Pd-In interactions but weaker Ca-Rh, Ca-Pd and Ca-In interactions. CaRhIn4 and Ca-PdIn4 are compared with other indium-rich compounds such as YCoIn5 and Y2CoIn8, and with elemental indium. Common structural motifs of the indium-rich compounds are distorted bcc-like indium cubes.