The fragmented nature of the influenza A genome allows the exchange of gene segments when two or more influenza viruses infect the same cell, but little is known about the rules underlying this process. Here, we studied genetic reassortment between the A/Moscow/10/99 (H3N2, MO) virus originally isolated from human and the avian A/Finch/England/2051/91 (H5N2, EN) virus and found that this process is strongly biased. Importantly, the avian HA segment never entered the MO genetic background alone but always was accompanied by the avian PA and M fragments. Introduction of the 5´ and 3´ packaging sequences of HA_MO into an otherwise HA_EN backbone allowed efficient incorporation of the chimerical viral RNA (vRNA) into the MO genetic background. Furthermore, forcing the incorporation of the avian M segment or introducing five silent mutations into the human M segment was sufficient to drive coincorporation of the avian HA segment into the MO genetic background. These silent mutations also strongly affected the genotype of reassortant viruses. Taken together, our results indicate that packaging signals are crucial for genetic reassortment and that suboptimal compatibility between the vRNA packaging signals, which are detected only when vRNAs compete for packaging, limit this process.