  Compressible, Riemann S-type ellipsoids can emit gravitational waves (GWs)
with a chirp-like behavior (hereafter chirping ellipsoids, CELs). We show that
the GW frequency-amplitude evolution of CELs (mass $\sim 1$~M$_\odot$, radius
$\sim10^3$~km, polytropic equation of state with index $n\approx 3$) is
indistinguishable from that emitted by double white dwarfs (DWDs) and by
extreme mass-ratio inspirals (EMRIs) composed of an intermediate-mass
(e.g.~$10^3~M_\odot$) black hole and a planet-like (e.g.~$10^{-4}~M_\odot$)
companion, in a specific frequency interval within the detector sensitivity
band in which the GWs of all these systems are quasi-monochromatic. We estimate
that for reasonable astrophysical assumptions, the rates in the local Universe
of CELs, DWDs and EMRIs in the mass range considered here, are very similar,
posing a detection-degeneracy challenge for space-based GW detectors. The
astrophysical implications of this CEL-binary detection degeneracy by
space-based GW-detection facilities, are outlined.
