  This note investigates a number of scenarios in which unadjusted testing
following a blinded sample size re-estimation leads to type I error violations.
For superiority testing, this occurs in certain small-sample borderline cases.
We discuss a number of alternative approaches that keep the type I error rate.
The paper also gives a reason why the type I error inflation in the superiority
context might have been missed in previous publications and investigates why it
is more marked in case of non-inferiority testing.
