The capture cross sections of 93Nb, 103Rh, and 181Ta were measured in the 10- to 70-keV neutron energy range, using 197Au as a standard. Most of the data points were obtained with a total uncertainty of ∼4%. This was possible because the calculation of capture gamma-ray spectra allowed reducing the most severe systematic uncertainties involved. Hauser-Feshbach calculations were performed that yielded not only the neutron cross sections of the isotopes considered up to 4-MeV neutron energy but also partial capture cross sections and capture gamma-ray spectra. For these calculations a consistent set of input parameters was determined from available experimental information or from model-guided systematics. The influence of these parameters on the results is discussed.