  For multiple testing based on p-values with c\`{a}dl\`{a}g distribution
functions, we propose an FDR procedure "BH+" with proven conservativeness. BH+
is at least as powerful as the BH procedure when they are applied to
super-uniform p-values. Further, when applied to mid p-values, BH+ is more
powerful than it is applied to conventional p-values. An easily verifiable
necessary and sufficient condition for this is provided. BH+ is perhaps the
first conservative FDR procedure applicable to mid p-values. BH+ is applied to
multiple testing based on discrete p-values in a methylation study, an HIV
study and a clinical safety study, where it makes considerably more discoveries
than the BH procedure.
