We show that the class of sets which can be polynomial
time truth table reduced to some $p$-superterse sets has
$p$-measure 0. Hence, no $P$-selective set is $\le_{tt}^p$-hard
for $E$. Also we give a partial affirmative answer to
the conjecture by Beigel, Kummer and Stephan. They conjectured
that every $\le_{tt}^p$-hard set for $NP$ is $P$-superterse
unless $P=NP$. We will prove that every $\le_{tt}^p$-hard set
for $NP$ is $P$-superterse unless $NP$ has $p$-measure $0$.