"Well, we would know for sure, if he places a fresh body on the Suffolk PD's doorsteps,"
Here's an interesting article written by a Miami Homicide detective. He talks about the Tamiami Strangler and how this SK was getting frustrated with police that they weren't connecting (or atleast admitting to the media) his victims to his work. I'm not sure if this belongs on this thread, but it is a very informative read for anyone who is interested.
"In the case of Rory Conde, nicknamed "The Tamiami Strangler," six prostitutes were found manually strangled and their bodies discarded at various locations near US-41, which in Miami is called Tamiami Trail. Conde's wife of many years lived in constant fear of beatings and abuse at Conde's hands. Once when his wife was absent Conde brought a prostitute home and dressed her in his wife's pajamas, videotaping their sex acts. When his wife eventually discovered the videotape, she moved out. The couple had several children and Conde had trouble visiting them as he tried to reconcile with his estranged wife. In his confession he blamed the prostitutes for his failed marriage and for losing his children.
Of the six people Conde killed, five were women and one was a transvestite. They were all prostitutes, picked up from within a few-blocks-square area known as a hangout for quick sex. Conde had sex with all of his victims and would strangle them during the sex act. The women were not beaten or brutalized; they all were strangled manually, with little other trauma. After killing his victims, he would often talk to the corpses, giving them advice-as though by such taking of extreme control he had made them "his." He would always re-dress the women after killing them and discard their bodies in locations such as residential neighborhoods, where they were easily discovered. Initially, when we discovered the second victim, we suspected a serial killer, but were not one hundred percent sure. This fact somehow made its way into the media and with his third victim,
Conde wrote a message on her back with a permanent magic marker, leaving us not doubt this was his third victim. Apparently Conde wanted the police to know and inform the media that he was responsible for all three killings. In this message he indicated he would call one of the local television anchors, but he never did. And his killings continued.
http://www.expertlaw.com/library/investigators/serial_killers.html