  In this paper we demonstrate that a double Michelson interferometer with
Fabry-Perot cavities in its arms is able to perform laser- and
displacement-noise-free gravitational-wave (GW) detection if certain model
assumptions are met. Assuming the input mirrors of a single
Michelson/Fabry-Perot interferometer can be rigidly attached to beamsplitter on
a central platform one can manipulate with interferometer's response signals in
a way to cancel laser noise and displacement noise of all test masses except
the cental platform. A pair of symmetrically positioned Michelson/Fabry-Perot
interferometers with common central platform can be made insusceptible to the
later then, thus allowing complete laser- and displacement-noise-free
interferometry (DFI). It is demonstrated that the DFI response to GWs of the
proposed interferometer is proportional to $f^2_{\textrm{gw}}/\gamma$, where
$\gamma$ is the cavity half-bandwidth, that is the strongest DFI response
allowed by general relativity.
