  We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT
where one copy of the seed CFT has been excited by a pair of oscillators, each
being either bosonic or fermionic. While such states are BPS at the orbifold
point, they will in general `lift' as the theory is deformed towards general
values of the couplings. We compute the expectation value of this lift at
second order in the deformation parameter for the above mentioned states. We
write this lift in terms of a fixed number of nested contour integrals on a
given integrand; this integrand depends on the mode numbers of the oscillators
in the state. We evaluate these integrals to obtain the explicit value of the
lift for various subfamilies of states. At large mode numbers one observes a
smooth increase of the lift with the dimension of the state $h$; this increase
appears to follow a $\sim \sqrt{h}$ behavior similar to that found analytically
in earlier computations for other classes of states.
