This paper introduces low-complexity block codes, termed pattern-eliminating codes (PEC), which achieve a potentially large performance improvement over channels with residual inter-symbol interference (ISI). The codes are systematic, require no decoding and allow for simple encoding. They operate by prohibiting the occurrence of harmful symbol patterns. On some discrete-time communication channels, the (n, n - 1) PEC can prohibit all occurrences of symbol patterns causing worst-case ISI. The effectiveness of a PEC is shown to be uniquely determined by the sign-signature of the channel response, and a simple criterion is given for identifying channels for which the (n, n-1) code is effective. It is also shown that for most channel signatures, the (n, n-1) PEC can be augmented by a (0, n-1) runlength-limiting (RLL) code at no additional coding overhead. This paper also explores properties of the (n, n-b) PEC for b > 1. The simulation results show that the (n, n-1) PEC can provide error-rate reductions of several orders of magnitude, even with rate penalty taken into account. It is also shown that channel conditioning, such as equalization, can have a large effect on the code performance and potentially large gains can be derived from optimizing the equalizer jointly with a pattern-eliminating code.