  We consider the problem of source compression under three different scenarios
in the one-shot (non- asymptotic) regime. To be specific, we prove one-shot
achievability and converse bounds on the coding rates for distributed source
coding, source coding with coded side information available at the decoder and
source coding under maximum distortion criterion. The one-shot bounds obtained
are in terms of smooth max Renyi entropy and smooth max Renyi divergence. Our
results are powerful enough to yield the results that are known for these
problems in the asymptotic regime both in the i.i.d. (independent and
identically distributed) and non-i.i.d. settings
