In this paper, partially systematic rate-compatible serial concatenated convolutional codes (SCCCs) are considered. These are generated from a classical rate 1/3 serial concatenated mother code. To obtain rate-compatible SCCCs, the puncturing is limited to inner coded bits, by puncturing both the inner code's parity and systematic bits. It is shown that the performance can be enhanced in the "waterfall" or in the "error-floor" region, by simply spreading the puncturing over the parity and the systematic bits without increasing encoding and decoding complexity.