We consider the transmissions of successive short packets. Each of them combines information to be transmitted (codeword) with information for synchronizing the frame (syncword). For short packets, the cost of including syncwords is no longer negligible and its design requires careful optimization. In particular, a trade-off arises depending on the way the total transmit power or the total frame length is split among the syncword and the codeword. As- suming optimal finite-length codes, we develop tight upper bounds on the probability of erroneous synchronization, for both frames with concatenated syncword and frames with superimposed syncword. We use these bounds to optimize this trade-off. Simulation results show that the proposed bounds and analysis have practical relevance for short packet communication system de- sign.