We have made precise final state interference measurements using very intense Mossbauer sources and an exact line-shape analysis. Two transitions in tungsten metal, as well as one in iridium metal and one in terbium oxide, have been studied. The interference parameters 100P found are -1.3 (3) for the 99.1-keV transition in W, -1. 2(1) for the 100.1-keV transition in W, -0.71(8) for the 129.4-keV transition in 'Ir, and -0.48(5) for the 58.0-keV transition in ' Tb. All values agreed with theory to within error. Our measurement of 1.16(2) cmjs for the ' 'Ir linewidth agrees with other Mossbauer measurements and shows no indication of hyperfine broadening, but disagrees with some non-Mossbauer measurements reported in the literature. The tungsten and terbium transitions also show no signs of broadening or splitting.PACS number(s): 23.20.Nx, 27.70. +q, 27.80.+w