Modern models of s-process nucleosynthesis in stars require stellar reaction rates of high precision. Most neutron-capture cross-sections in the s-process have been measured, and for an increasing number of reactions the required precision is achieved. This does not necessarily mean, however, that the stellar rates are constrained equally well, because only the capture of the ground state of a target is measured in the laboratory. Captures of excited states can contribute considerably to stellar rates that are already at typical s-process temperatures. We show that the ground-state contribution X to a stellar rate is the relevant measure to identify reactions that are or could be well constrained by experiments and apply it to (n,gamma) reactions in the s-process. We further show that the maximum possible reduction in uncertainty of a rate via determination of the ground-state cross-section is given directly by X. An error analysis of X is presented, and it is found that X is a robust measure with mostly small uncertainties. Several specific examples (neutron capture of Se-79, Zr-95, Sn-121, Os-187, and Pt-193) are discussed in detail. The ground-state contributions for a set of 412 neutron-capture reactions around the s-process path are presented in a table. This allows identification of reactions that may be better constrained by experiments and that cannot be constrained solely by measuring ground-state cross-sections (and thus require supplementary studies). General trends and implications are discussed.