  We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT
where we excite one copy of the seed CFT with a left-moving superconformal
descendant. When the theory is deformed away from this region of moduli space
these states can `lift', despite being BPS at the orbifold point. For
descendants formed from the supersymmetry $G^{\alpha}_{\!\dot{A},-s}$ and
R-symmetry $J^a_{-n}$ current modes we obtain explicit results for the
expectation value of the lifts for various subfamilies of states at second
order in the deformation parameter. A smooth $\sim\sqrt{h}$ behaviour is
observed in the lifts of these subfamilies for large dimensions. Using covering
space Ward identities we then find a compact expression for the lift of the
above $J^a_{-n}$ descendant states valid for arbitrary dimensions. In the
large-dimension limit this lift scales as $\sim\sqrt{h}\,$, strengthening the
conjecture that this is a universal property of the lift of D1-D5-P states. We
observe that the lift is not simply a function of the total dimension, but
depends on how the descendant level is partitioned amongst modes.
