We consider Multimessage Multicasting over the n processor complete (or fully connected) static network (MMC). We present several fast approximation algorithms with improved approximation bounds for problem instances with small fan-out (maximum number of processors receiving any given message), but arbitrary degree d, where d is the maximum number of messages that each processor may send (receive). These problem instances are the ones that arise in practice, since the fan-out restriction is imposed by the applications and the number of processors available in commercial systems.