In this paper, we present some results of the search for good partially systematic rate-compatible punctured turbo codes (RCPTC) and compare them with classical systematic RCPTCs. Partially systematic RCPTCs can achieve lower error floors than systematic RCPTCs, because of their superior free distance properties. Moreover, they can achieve comparable performance in the waterfall region if the design of the puncturing scheme is carefully addressed. The two main applications of this technique are its use in hybrid incremental ARQ/FEC schemes and to achieve unequal error protection of an information sequence.