We consider Toeplitz operators in different Bergman type spaces, having
radial symbols with variable sign. We show that if the symbol has compact
support or decays rapidly, the eigenvalues of such operators cannot decay too
fast, essentially faster than for a sign-definite symbol with the same kind. On
the other hand, if the symbol decays not sufficiently rapidly, the eigenvalues
of the corresponding operator may decay faster than for the operator
corresponding to the absolute value of the symbol.