For soft-input soft-output sphere decoding (SD), the combination of the Schnorr-Euchner (SE) enumeration and the radius reduction shrink the search space quickly but with considerable computational complexity. In this paper, a low complexity approach is proposed to reduce the tree search space before SD starts. Particularly, such reduction is achieved by 1) tightening the initial radius; 2) restricting the search space to a subset of the symbol lattice. With further enhancement on the tree pruning constraint, simulation results demonstrate significant complexity savings with negligible error rate performance loss.