We　have　studied　the　one-step　procedure　for　simultaneous　synthesis　and　sintering　of　SiC-doped　MgB2　by　the　spark　plasma　sintering　technique.　Two　types　of　composition,　one　in　which　Mg　is　strongly　deficient,　with　the　atomic　ratio　,　and　one　in　which　Mg　content　is　slightly　higher　than　the　stoichiometric　value,　specifically　,　were　investigated.　The　amount　of　SiC　was　12　wt.%　and　9　wt.%,　respectively.　For　comparison　we　also　studied　the　way　the　deficit　of　Mg　can　be　compensated　in　a　second　process　of　sintering.　The　sample　with　Mg　deficit　shows　that　SiC　is　left　almost　unreacted　but　the　results　are　spectacular:　the　highest　critical　temperature,　36.5　K,　the　highest　upper　critical　field　and　the　highest　self-field　critical　current　density　6.7x10(5)　A/cm(2)　at　10　K.　In　the　sample　with　overstoichiometric　Mg,　SiC　is　decomposed,　carbon　diffuses　within　MgB2　but　the　critical　temperature　is　only　of　35.8　K　and　the　zero-field　critical　current　density　is　one　order　of　magnitude　lower.　The　compensation　of　the　deficit　of　Mg　in　the　two-step　procedure　is　not　efficient.　The　critical　temperature　is　even　lower,　35.8　K,　the　upper　critical　field　is　also　lower　despite　SiC　decomposition　and　C　diffusion　within　MgB2　and　the　critical　current　density　is　slightly　above　10(5)　A/cm(2).　However,　at　low　temperatures　and　fields　of　order　7　T　the　sample　with　overstoichiometric　Mg　and　the　sample　prepared　by　the　two-step　procedure　have　higher　critical　current　density.