  The running infimum of a Levy process relative to its point of issue is know
to have the same range that of the negative of a certain subordinator.
Conditioning a Levy process issued from a strictly positive value to stay
positive may therefore be seen as implicitly conditioning its descending ladder
heigh subordinator to remain in a strip. Motivated by this observation, we
consider the general problem of conditioning a subordinator to remain in a
strip. Thereafter we consider more general contexts in which subordinators
embedded in the path decompositions of Markov processes are conditioned to
remain in a strip.
