  Detection of gravitational-wave (GW) sources enables the characterisation of
binary compact objects and of their in-spiral. However, other dissipative
processes can affect the in-spiral. Here we show that the in-spiral of compact
objects through a gaseous common-envelope (CE) arising from an evolved stellar
companion produces a novel type of GW-sources, whose evolution is dominated by
the dissipative gas dynamical friction effects from the CE, rather than the
GW-emission itself. The evolution and properties of the GW-signals differ from
those of isolated gas-poor mergers significantly. We find characteristic
strains of $\sim10^{-23}$-$10^{-21}$ ($10{\rm kpc}/{D}$) for such sources --
observable by next-generation space-based GW-detectors. The evolution of the
GW-signal can serve as a probe of the interior regions of the evolved star, and
the final stages of CE-evolution, otherwise inaccessible through other
observational means. Moreover, such CE-mergers are frequently followed by
observable explosive electromagnetic counterparts and/or the formation of
exotic stars.
