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.