  The Konishi superconformal multiplet is an important theoretical laboratory
where one can test AdS/CFT methods to compute strong coupling corrections to
the spectrum of superstrings in AdS_5 x S^5. In particular, one can exploit
integrability for finite charge states/operators. The multiplet ground state is
a singlet operator with two simple descendants in the rank-1 sectors sl(2) and
su(2) of N=4 super Yang-Mills theory. Recently, the next-to-leading quantum
correction to the sl(2) state has been computed. Here, we use the algebraic
curve approach to determine the correction to the other state recovering
universality of the correction inside the multiplet.
