  We propose a detuned Fabry-Perot cavity, pumped through both the mirrors, as
\textit{a toy model} of the gravitational-wave (GW) detector partially free
from displacement noise of the test masses. It is demonstrated that the noise
of cavity mirrors can be eliminated, but the one of lasers and detectors
cannot. The isolation of the GW signal from displacement noise of the mirrors
is achieved in a proper linear combination of the cavity output signals. The
construction of such a linear combination is possible due to the difference
between the reflected and transmitted output signals of detuned cavity. We
demonstrate that in low-frequency region the obtained displacement-noise-free
response signal is much stronger than the $f^3_{\textrm{gw}}$-limited
sensitivity of displacement-noise-free interferometers recently proposed by S.
Kawamura and Y. Chen. However, the loss of the resonant gain in the noise
cancelation procedure results is the sensitivity limitation of our toy model by
displacement noise of lasers and detectors.
