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For every total recursive time bound $t$, a constant fraction of allcompressible (low Kolmogorov complexity) strings is $t$-bounded incompressible(high time-bounded Kolmogorov complexity); there are uncountably many infinitesequences of which every initial segment of length $n$ is compressible to $\logn$ yet $t$-bounded incompressible below ${1/4}n - \log n$; and there arecountable infinitely many recursive infinite sequence of which every initialsegment is similarly $t$-bounded incompressible. These results are related to,but different from, Barzdins's lemma.

On Time-Bounded Incompressibility of Compressible Strings and Sequences