For relativized arguments,
we propose to restrict oracle queries to ``stringent'' ones;
for comparing the power of two machine models relative to some oracle set,
stringent relativization is
to restrict machines of both types
to ask queries on the same segment of the oracle.
In particular,
for investigating polynomial-time (or polynomial-size) computability,
we propose polynomial stringency,
bounding query length to any fixed polynomial of input length.
Under such stringent oracle access,
we show an oracle G
such that BPP(G) = PH(G).