  We probe the ability of various types of post-Newtonian(PN)-accurate circular
templates to capture inspiral gravitational-wave (GW) signals from compact
binaries having tiny orbital eccentricities. The GW signals are constructed by
adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R.
Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the
time-eccentricity to describe the orbital evolution. Using the fitting factor
estimates, relevant for the initial LIGO, we show that circular templates,
based on the adiabatic TaylorT1, complete adiabatic TaylorT1 and TaylorT4
approximants are unable to capture our GW signals from compact binaries having
tiny residual orbital eccentricities. However, the 2PN-order circular inspiral
templates based on the recently introduced TaylorEt approximant are found to be
both effectual and faithful in capturing GWs from inspiralling compact binaries
having moderate eccentricities and we provide physical explanations for our
observations.
