  We provide new false discovery proportion (FDP) confidence envelopes in
several multiple testing settings relevant to modern high dimensional-data
methods. We revisit the scenarios considered in the recent work of
\cite{katsevich2020simultaneous}(top-$k$, preordered -- including knockoffs --
, online) with a particular emphasis on obtaining FDP bounds that have both
non-asymptotical coverage and asymptotical consistency, i.e. converge below the
desired level $\alpha$ when applied to a classical $\alpha$-level false
discovery rate (FDR) controlling procedure. This way, we derive new bounds that
provide improvements over existing ones, both theoretically and practically,
and are suitable for situations where at least a moderate number of rejections
is expected. These improvements are illustrated with numerical experiments and
real data examples. In particular, the improvement is significant in the
knockoff setting, which shows the impact of the method for practical use. As
side results, we introduce a new confidence envelope for the empirical
cumulative distribution function of i.i.d. uniform variables and we provide new
power results in sparse cases, both being of independent interest.
