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We study quantitative versions of the Schur property and weak sequentialcompleteness, proceeding thus with investigations started by G. Godefroy, N.Kalton and D. Li and continued by H. Pfitzner and the authors. We show that theSchur property of $\ell_1$ holds quantitatively in the strongest possible wayand construct an example of a Banach space which is quantitatively weaklysequentially complete, has the Schur property but fails the quantitative formof the Schur property.

On a difference between quantitative weak sequential completeness and the quantitative Schur property