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This paper extends and fully formalizes some previous results by developing an analytical method to account for the general chip pulse for DS-CDMA systems in an asynchronous environment with an integrate-and-dump receiver, applying it to commonly used pulses. Given the pulse, such a formal method allows us to define the optimum spreading code autocorrelation to be used and the relative signal-to-interference ratio performance. A chaos-based spreading code is plugged into this model to show that such an optimum performance can be very well approximated by practical sequence generators. This is shown by analyzing some typical bandlimited and substantially bandlimited pulses and determining the optimum spreading for each of them. These results prove that the gain of chaos-based spreading over conventional i.i.d.-like spreading can reach 75% when practical bandlimited pulses are considered.