A weak pseudorandom function (wPRF) is a cryptographic primitive similar to ? but weaker than ? a pseudorandom function: for wPRFs one only requires that the output is pseudorandom when queried on random inputs. We show that unlike "normal" PRFs, wPRFs are seedincompressible, in the sense that the output of a wPRF is pseudorandom even if a bounded amount of information about the key is leaked. As an application of this result we construct a simple mode of operation which ? when instantiated with any wPRF ? gives a leakage-resilient stream-cipher. The implementation of such a cipher is secure against every side-channel attack, as long as the amount of information leaked per round is bounded, but overall can be arbitrary large. The construction is simpler than the previous one (Dziembowski-Pietrzak FOCS'08) as it only uses a single primitive (a wPRF) in a straight forward manner.