A hitting-set generator is a deterministic
algorithm which generates a set of strings that intersects
every dense set recognizable by a small circuit.
A polynomial time hitting-set generator readily implies $RP=P$.
Andreev \etal\/ (ICALP'96, and JACM 1998)
showed that if polynomial-time hitting-set
generator in fact implies the much stronger conclusion $BPP=P$.
We simplify and improve their (and later) constructions.