  Self-stimulated echoes have recently been reported in the high cooperativity
and inhomogeneous coupling regime of spin ensembles with superconducting
resonators. In this work, we study their relative amplitudes using
echo-silencing made possible by a fast frequency tunable resonator. The highly
anisotropic spin linewidth of Er$^{3+}$ electron spins in the CaWO$_4$ crystal
also allows to study the dependence on spin-resonator ensemble cooperativity.
It is demonstrated that self-stimulated echoes primarily result from a
combination of two large control pulses and the echo preceding it.
