The incongruently melting single-filled skutterudite InxCo4Sbi2 is known as a promising bulk thermoelectric material. However, the products of current bulk syntheses contain always impurities of InSb, Sb, CoSb, or CoSb2, which prevent an unbiased determination of its thermoelectric properties. We report a new two-step synthesis of high-purity InxCo4Sbi2 with nominal compositions x = 0.12, 0.15, 0.18, and 0.20 that separates the kieftite (CoSb3) formation from the topotactic filler insertion. This approach allows conducting the reactions at lower temperatures with shorter reaction times and circumventing the formation of impurity phases. The synthesis can be extended to other filled skutterudites. High-density (>98%) pellets for thermoelectric characterization were prepared by current-assisted short-time sintering. Sample homogeneity was demonstrated by potential and Seebeck microprobe measurements of the complete pellet surfaces. Synchrotron X-ray diffraction showed a purity of 99.9% product with traces (<0.1%) of InSb in samples of nominal composition In0.18Co4Sb12 and In0.20Co4Sb12. Rietveld refinements revealed a linear correlation between the true In occupancy and the lattice parameter a. This allows the determination of the true In filling in skuttenidites and predicting the In content of unknown A Co4Sb12. The high purity of In(x)Co(4)Sbi(2) allowed studying the transport properties without bias from side phases. A figure of merit close to unity at 420 degrees C was obtained for a sample of a true composition of In-0.60(2)Co4Sb12 (nominal composition In0.18Co4Sb12). The lower degree of In filling has a dramatic effect on the thermoelectric properties as demonstrated by the sample of nominal composition In0.20Co4Sb12. The presence of InSb in amounts of similar to 0.1 vol% led to a substantially lower degree of interstitial site filling of 0.144, and the figure of merit zT decreased by 18%, which demonstrates the significance of the true filler atom content in skutterudite materials.