In4Se3-x　compound　is　considered　as　a　potential　thermoelectric　material　due　to　its　comparably　low　thermal　conductivity　among　all　existing　ones.　While　most　studies　investigated　In4Se3-x　thermoelectric　properties　by　controlling　selennium　or　other　dopants　concentrations,　in　the　current　study,　it　was　found　that　even　for　a　fixed　initial　In/Se　ratio,　the　resulting　In/Se　ratio　varied　significantly　with　different　thermal　processing　histories　(i.e.,　melting　and　annealing),　which　also　resulted　in　varied　thermoelectric　properties　as　well　as　fracture　surface　morphologies　of　In4Se3-x　polycrystalline　specimens.　Single　phase　polycrystalline　In4Se3-x　compounds　were　synthesized　by　combining　a　sequence　of　melting,　annealing,　pulverizing,　and　spark　plasma　sintering.　The　extension　of　previous　thermal　history　was　observed　to　significantly　improve　the　electrical　conductivity　(about　121%)　and　figure　of　merit　(about　53%)　of　In4Se3-x　polycrystalline　compounds.　The　extended　thermal　history　resulted　in　the　increase　of　Se　deficiency　(x)　from　0.39　to　0.53.　This　thermally　induced　Se　deficiency　was　observed　to　associate　with　increasing　carrier　mobility　but　decreasing　concentration,　which　differs　from　the　general　trend　observed　for　the　initially　adjusted　Se　deficiency　at　room　temperature.　Unusually　large　dispersed　grains　with　nanosize　layers　were　observed　in　specimens　with　the　longest　thermal　history.　The　mechanism(s)　by　which　previous　thermal　processing　enhances　carrier　mobility　and　affect　microstructural　evolution　are　briefly　discussed.