For relativized arguments,
we propose to restrict oracle queries to ``stringent" ones.
For example,
when comparing the power of two machine models relative to some oracle set X,
we restrict that
machines of both types ask queries
from the same segment of the set X.
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, for example,
an oracle G such that P(G) = Sigma_d^p(G),
for any constant d >= 1.