Schwan

From a more practical point of view, and please, don't freak out, it's something that I know a bit about due to what I study, you'd certainly have to:

a) commit the actual murder in a place where organic left overs, so to speak, are not out of ordinary. I'm talking forests, areas where there is not roads and dwellings. The person shouldn't be able to pu up a struggle, at least in a manner that would leave ANY organic (eg. skin tissue, blood) marks on objects that come from your surrounding: car, clothes, etc. I guess at this point that drugs might be involved.

b) getting rid of the body is the second thing, since most of the investigators come to conclusion about murderers based on the damage that they found on the body. How to get rid of a body is something else completely, but the key is that nothing should be left.

c) finally, there is the connection problem. Fatc is, if you're somehow connected to that person, in any way possible, make it casual meetings on the street or something like that, you're 90% more likely to be caught. As someone said, randomizing the whole event is the key.

Having said that, I'd like to point out it's hard to do any research on the topic, because of the definition of "perfect murder", since it's, well, perfect, and we don’t know about it. We have no clue who did it, when and how, unless they admit to it themselfes. All of these guesses, therefore, are based on the view from the other side of the barricade, the investigators side, and therefore not completely accurate.

I also have to say that even writing about this stuff is eerie, but so is life most of the time. I wouldn't want anyone to even try these things out on someone and, anyway, the fact is that sooner or later, a murderer would break down or would continue to kill until he'd make a mistake, as someone pointed out. it's only a matter of time.