The compression-mode isoscalar giant monopole resonance (ISGMR) has been studied in the Sn, Cd and Pb isotopes using inelastic scattering of 400 MeV α-particles at extreme forward angles, including 0°. We have obtained completely "background-free" inelastic-scattering spectra for the Sn, Cd, and Pb isotopes for a wide angular and excitation-energy range. The various giant resonances excited with different transferred angular momenta were extracted by a multipole-decomposition analysis (MDA). It was found that the centroid energies of the ISGMR in Sn isotopes are significantly lower than the theoretical predictions. The Kτ in the empirical expression for the nuclear incompressibility has been determined to be Kτ=- 550±100MeV for the Sn isotopes. The extracted value for the Cd isotopes is Kτ=-480±100MeV. These numbers are consistent with values of Kτ=-370±120MeV obtained from an analysis of the isotopic transport ratios in medium-energy heavy-ion reactions, K τ=-500-100+120MeV obtained from constraints placed by neutron-skin data from anti-protonic atoms across the mass table, and Kτ=-500±50MeV obtained from theoretical calculations using different Skyrme interactions and relativistic mean field (RMF) Lagrangians. Stringent constraints on interactions employed in nuclear structure calculations are obtained on the basis of the experimentally determined values for K∞ and Kτ. These parameters constrain as well the equation of state (EOS) of nuclear matter. However, a significant discrepancy still remains. The ISGMR positions in Sn and Cd isotopes are systematically lower than the predictions obtained on basis of determined from the ISGMR in 208Pb. This raises the question "Why are Sn and Cd nuclei so soft?". For a clue to solve the problem, we discuss the preliminary results on the exact positions of the ISGMR in 204,206,208Pb.