Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the same relative post-Newtonian order form the basis of the standard adiabatic approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new complete adiabatic approximant constructed from the energy and flux functions. At the leading order, it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively, the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the effectualness at lower PN (<3PN) orders, while standard approximants of order ≥3PN provide a good lower bound to the complete approximants for the construction of effectual templates. Faithfulness of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri.