We study the problem of computing optimal spaced seeds for detecting sequences generated by a Hidden Markov model. Inspired by recent work in DNA sequence alignment, we have developed such a model for representing the conservation between related DNA coding sequences. Our model includes positional dependencies and periodic rates of conservation, as well as regional deviations in overall conservation rate. We show that, for hidden Markov models in general, the probability that a seed is matched in a region can be computed efficiently, and use these methods to compute the optimal seed for our models. Our experiments on real data show that the optimal seeds are substantially more sensitive than the seeds used in the standard alignment program BLAST, and also substantially better than those of PatternHunter or WABA, both of which use spaced seeds. Our results offer the hope of improved gene finding due to fewer missed exons in DNA/DNA comparison, and more effective homology search in general, and may have applications outside of bioinformatics.