Statistics for large k-mers with low counts

Question

[schlogl]

Suppose I have a big genome and a small one (ex. mitochondrion) And I would like to know which words are under-over represented in both, but using a high Markov model (Rocha et al.) led to a powerless statistic tests, because of low counts, when using bigger k lengths. Any of the friends have a suggestion of a different or robust model to access this comparison? Thanks in advance. Paulo