We analyze a generalization of a recent algorithm of Bleichenbacher et al.~for decoding interleaved codes on the $Q$-ary symmetric channel for large $Q$. We will show that for any $m$ and any $\epsilon$ the new algorithms can decode up to a fraction of at least $\frac{\beta m}{\beta m+1}(1-R-2Q^{- 1/2m})-\epsilon$ errors (where $\beta = \frac{\ln(q^m - 1)}{\ln(q^m)}$), and that the error probability of the decoder is upper bounded by $O(1/q^{\epsilon n})$, where $n$ is the block-length. The codes we construct do not have a- priori any bound on their length.