  The space-based detector LISA may observe gravitational waves from the early
inspiral of stellar-mass black hole binaries, some of which could have
significant eccentricity. Current gravitational waveform templates are only
valid for small orbital velocities (i.e., in a post-Newtonian expansion) and
small initial eccentricity $e_0$ ("post-circular" expansion). We conventionally
define $e_0$ as the eccentricity corresponding to an orbital frequency of $5
\text{ mHz}$, and we study the convergence properties of frequency-domain
inspiral templates that are accurate up to 2PN and order $e_0^6$ in
eccentricity. We compute the so-called "unfaithfulness" between the full
template and "reduced" templates obtained by dropping some terms in the phasing
series; we investigate the conditions under which systematic errors are
negligible with respect to statistical errors, and we study the convergence
properties of statistical errors. In general, eccentric waveforms lead to
larger statistical errors than circular waveforms due to correlations between
the parameters, but the error estimates do not change significantly as long as
we include terms of order $e_0^2$ or higher in the phasing.
