Westudyanonlinearlosslesspolarizer(NLP),afiber-baseddeviceabletocontrolthepolarizationofanopticalsignalwhilepreservingitsenergy.TheNLPexploitsthelosslesspolarizationattraction(LPA)generatedbytheKerrinteractionsbetweenthesignalandafullypolarizedcontinuouswave(CW)pump.Byemployingacopropagatingpump,weshowthattheeffectivenessofLPAdependsonthejointactionoftheKerrnonlinearityandthemutualdelaybetweensignalandpump.WefindtheoptimalpumpwavelengthplacementanddemonstratethattrueLPAoccursonlywithinalimitedrangeofdelayvalues.Thus,weexplainwhythecopropagatingNLPismoreflexibleandpowerefficientcomparedwiththetraditionalcounterpropagatingNLP.