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In a recent investigation of the effects of precession on the anticipateddetection of gravitational-wave inspiral signals from compact object binarieswith moderate total masses, we found that (i) if precession is ignored, theinspiral detection rate can decrease by almost a factor of 10, and (ii)previously proposed ``mimic'' templates cannot improve the detection ratesignificantly (by more than a factor of 2). In this paper we propose a newfamily of templates that can improve the detection rate by factors of 5--6 incases where precession is most important. Our proposed method for these new``mimic'' templates involves a hierarchical scheme of efficient, two-parametertemplate searches that can account for a sequence of spikes that appear in theresidual inspiral phase, after one corrects for the any oscillatorymodification in the phase. We present our results for two cases of compactobject masses (10 and 1.4 solar masses and 7 and 3 solar masses) as a functionof spin properties. Although further work is needed to fully assess thecomputational efficiency of this newly proposed template family, we concludethat these ``spiky templates'' are good candidates for a family of precessiontemplates used in realistic searches, that can improve detection rates ofinspiral events.Comment: 17 pages, 22 figures, version accepted by PRD. Minor revision

Searching for gravitational waves from the inspiral of precessing binary systems: New hierarchical scheme using “spiky” templates