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Less nonstationary ideals

We are proving the following: (1) If $\kap$ is a weakly inaccessible then $NS_\kap$ is not $\kap^+$-saturated. (2) If $\kap$ is a weakly inaccessible and $\tet <\kap$ is regular then $NS^\tet_\kap$ is not $\kap^+$-saturated. (3) If $\kap$ is singular then $NS^{cf\kap}_{\kap^+}$ is not $\kap^{++}$-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If $\kap >\aleph_1$ then $NS_\kap$ is not $\kap^+$-saturated. (B) If $\tet^+<\kap$ then $NS^\tet_\kap$ is not $\kap^+$-saturated.