  We present a four parameter family of classical string solutions in AdS_3 x
S^3, which end along a light-like tetragon at the boundary of AdS_3 and carry
angular momentum along two cycles on the sphere. The string surfaces are
space-like and their projections on AdS_3 and on S^3 have constant mean
curvature. The construction is based on the Pohlmeyer reduction of the related
sigma model. After embedding in AdS_5 x S^5, we calculate the regularized area
and analyze conserved charges. Comments on possible relations to scattering
amplitudes are presented. We also sketch time-like versions of our solutions.
