Let (X; d) be a metric space. The sets A; B ⊂ X are said to be wobbling equivalent if there is a bijection f mapping A onto B such that sup x 2 A d(x; f(x)) < 1 . The space is called paradoxical if there is a decomposition X =X1 [X2 such that X1;X2 and X are pairwise wobbling equivalent. W. A. Deuber, M. Simonovits and V. T. Sos proved that a discrete and countable metric space (X; d) is paradoxical if and only if there is an r≯0 such that jf x 2 X : dist(x; H) 5 r gj = 2 j H j holds for every finite H ⊂ X. We generalize this result for arbitrary metric spaces, more- over, for a more general class of spaces (called bounded spaces)in whichthenotion of wobbling equivalence can be formulated in a reasonable way.