  We study the phenomenological consequences of amplitude-corrected
post-Newtonian (PN) gravitational waveforms, as opposed to the more commonly
used restricted PN waveforms, for the quasi-circular, adiabatic inspiral of
compact binary objects. In the case of initial detectors it has been shown that
the use of amplitude-corrected waveforms for detection templates would lead to
significantly lower signal-to-noise ratios (SNRs) than those suggested by
simulations based exclusively on restricted waveforms. We further elucidate the
origin of the effect by an in-depth analytic treatment. The discussion is
extended to advanced detectors, where new features emerge. Non-restricted
waveforms are linear combinations of harmonics in the orbital phase, and in the
frequency domain the $k$th harmonic is cut off at $k f_{LSO}$, with $f_{LSO}$
the orbital frequency at the last stable orbit. As a result, with
non-restricted templates it is possible to achieve sizeable signal-to-noise
ratios in cases where the dominant harmonic (which is the one at twice the
orbital phase) does not enter the detector's bandwidth. This will have
important repercussions on the detection of binary inspirals involving
intermediate-mass black holes. For sources at a distance of 100 Mpc, taking
into account the higher harmonics will double the mass reach of Advanced LIGO,
and that of EGO gets tripled. Conservative estimates indicate that the
restricted waveforms underestimate detection rates for intermediate mass binary
inspirals by at least a factor of twenty.
