  We construct solutions of IIB supergravity dual to non-supersymmetric states
of the D1D5 system. These solutions are constructed as perturbations carrying
both left and right moving momentum around the maximally rotating D1D5 ground
state at linear order. They are found by extending to the asymptotically flat
region the geometry generated in the decoupling limit by the action of left and
right R-currents on a known D1D5 microstate. The perturbations are regular
everywhere and do not carry any global charge. We also study the near-extremal
limit of the solutions and derive the first non-trivial correction to the
extremal geometry.
