The properties of weak sources of randomness have been investigated in many contexts and using several models of weakly random behaviour. For two such models, developed by Santha and Vazirani, and Chor and Goldreich, it is known that the output from one such source cannot be "compressed" to produce nearly random bits. At the same time, however, a single source is sufficient to solve problems in the randomized complexity classes BPP and RP. It is natural to ask exactly which tasks can be done using a single, weak source of randomness and which cannot. The present work begins to answer this question by establishing that a single weakly random source of either model cannot be used to obtain a secure "one-time-pad" type of cryptosystem.