If a certain number of receiver processors (RPs) are reserved exclusively for new calls, some decrease in the probability of blocking new calls (Pn) can be obtained at the expense of increase in dropping handoff calls (Ph). This kind of prioritization has been often considered for handoff calls. Since soft handoff in CDMA systems results in sufficiently low Ph, an idea of prioritizing new calls is interesting when admitting more originating traffic into the system is relatively beneficial, which will be further investigated in this paper. An obvious constraint of the above idea is that Ph should be maintained below a given requirement. We formulate the proposed scheme as a mathematical programming problem and prove it improves the performance in terms of weighted carried traffic. As a result of this work, the prioritization of new calls is shown to possibly improve the traffic-carrying performance of a CDMA base station (BS) while maintaining an acceptable level of Ph, which can be prespecified by a system engineer.