In past decades a lot of progress has been made towards understanding the main s-process component that takes place in thermally pulsing Asymptotic Giant Branch (AGB) stars. During this process about half of the heavy elements, mainly between 90 ≤ A ≤ 209 are synthesized. Improvements were made in stellar modeling as well as in measuring relevant nuclear data for a better description of the main s process. The weak s process, which contributes to the production of lighter nuclei in the mass range 56 ≤ A ≤ 90 operates in massive stars (M ≥ 8 M_⊙) and is much less understood. A better characterization of the weak s component would help disentangle the various contributions to element production in this region. For this purpose, a series of measurements of neutron-capture cross sections have been performed on medium-mass nuclei at the 3.7-MV Van de Graaff accelerator at FZK using the activation method. Also, neutron captures on abundant light elements with A < 56 play an important role for s-process nucleosynthesis, since they act as neutron poisons and affect the stellar neutron balance. New results are presented for the (n, γ) cross sections of ⁴¹K and ⁴⁵Sc, and revisions are reported for a number of cross sections based on improved spectroscopic information.