In order to save storage resource, our previous paper investigated the problem of compressing strings (i.e., only keeping part of the original string) while tracking the behaviour of the given discrete event system. Recoverability was first proposed, which requires the original string can be undoubtedly reconstructed from the compressed string. If an original string itself is recoverable, then we say it is compressible. However, our previous paper can only compress a compressible string. In this paper, a new notion of k-step lossless compression is proposed. It says that the last k events in a k-step compressed string are also the last k events of the original string and all events before might be compressed in any desirable way. For any given original string, our results show that there always exists the minimal k such that the given original string is k-step compressible. We propose algorithms to determine the minimal k and calculate a minimally k-step recoverable compressed string for the given original string.