  We study energy critical one-equivariant wave maps taking values in the
two-sphere. It is known that any finite energy wave map that develops a
singularity does so by concentrating the energy of (possibly) several copies of
the ground state harmonic map at the origin. If only a single bubble of energy
is concentrated, the solution decomposes into a dynamically rescaled harmonic
map plus a term that accounts for the energy that radiates away from the
singularity. In this paper, we construct blow up solutions by prescribing the
radiative component of the map. In addition, we give a sharp classification of
the dynamical blow up rate for every solution with this prescribed radiation.
