Recently (Crypto’24), Das and Ren proposed an adaptively secure variant of threshold BLS signatures. Unlike the initial threshold BLS signature described by Boldyreva (PKC’03), their variant can be proven secure in the adaptive corruption setting while preserving the useful features of the scheme (i.e., non-interactivity, uniqueness of signatures, and optimal signature size). In this work, we present a simplification of their scheme where the sizes of partial signatures and secret key shares are decreased by \(\approx 20 \%\) and \(33 \%\) , respectively. In addition, we reduce the communication cost of the distributed key generation phase by a factor 2. We can still prove the security of our simplified variant under adaptive corruptions in the random oracle model and under the same assumptions (namely, the co-CDH assumption and the DDH assumption in the first source group of the pairing) as Das and Ren.