We consider uniform assumptions for derandomization. We provide intuitive evidence that BPP can be simulated non-trivially in deterministic time by showing that (1) P \not \subseteq i.o.i.PLOYLOGSPACE implies BPP \subseteq SUBEXP (2) P \not \subseteq SUBPSPACE implies BPP = P. These results extend and complement earlier work of Sipser, Nisan- ... more >>>