$^{31}$Si was produced through the $^{18}$O ($^{18}$O, $\alpha$n) reaction at the beam energy of 25 MeV, which preferentially populates the high spin states. The $\alpha$ particles were detected in Microball and the multiple $\gamma$-ray coincidences were detected by Gammashpere. Event by event kinematic correction of the $^{31}$Si recoil energies and angles using information from Microball on the energies and angles of the $\alpha$ evaporations led to a better Doppler correction, which allowed us to discover 5 more new states and 15 new transitions in addition to the 11 more states and 22 $\gamma$ transitions found before kinematic correction compared to earlier works. A strong competition is seen between negative-parity ``intruder'' states and positive-parity pure s-d states. Shell model calculations agree relatively well with both groups of states.
*Supported in part by the U.S. National Science Foundation under grant NSF-10-64819.
