  Classical simulations of noisy stabilizer circuits are often used to estimate
the threshold of a quantum error-correcting code. Physical noise sources are
efficiently approximated by random insertions of Pauli operators. For a single
qubit, more accurate approximations that still allow for efficient simulation
can be obtained by including Clifford operators and Pauli operators conditional
on measurement in the noise model. We examine the feasibility of employing
these expanded error approximations to obtain better threshold estimates. We
calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for
amplitude damping and dephasing along a non-Clifford axis. The expanded
channels estimate the actual channel action more accurately than the Pauli
channels before error correction. However, after error correction, the Pauli
twirling approximation yields very accurate estimates of the performance of
quantum error-correcting protocols in the presence of the actual noise channel.
