  We provide analytical composite pulse sequences that perform dynamical
decoupling concurrently with arbitrary rotations for a qubit coded in the spin
state of a triple quantum dot. The sequences are designed to respect realistic
experimental constraints such as strictly nonnegative couplings. Logical errors
and leakage errors are simultaneously corrected. A short pulse sequence is
presented to compensate nuclear noise and a longer sequence is presented to
simultaneously compensate nuclear and charge noise. The capability developed in
this work provides a clear prescription for combatting the relevant sources of
noise that currently hinder exchange-only qubit experiments.
