The Webber and Henyey-Pumplin lower bounds on the root-mean-square impact parameter of exclusive K +p reactions are determined and compared with the slope of the overlap function calculated from uncorrelated-particle-production models. The similarity of the lower bounds obtained with different methods is shown to be a consequence of the nearly Gaussian transverse-momentum structure of the reaction matrix element squared at fixed rapidities. Multiplicity and total-energy dependence follow naturally from the dynamical transverse-momentum limitation and phase space. The weakness of the lower bounds constitutes evidence for important phase and/or spin contributions to the average squared impact parameter.