As 2Samuel (which, as I think I said earlier, was not really a separate book originally) begins, we have yet another story about Amalekites. An Amalekite comes to David and claims that he has killed Saul, prompting the SAB to ask how it could be possible for an Amalekite to exist, given the history of various attempts throughout the reign of Saul to obliterate them. Note however that right here in this chapter, the very first verse mentions David's "slaughter of the Amalekites". I think it would be quite a stretch to claim that the author of this passage didn't notice this juxtaposition as he wrote it. That being the case, I take it as my understanding that all these military attempts at wiping out the Amalekites keep managing to miss a few. David has clearly missed at least one.
Although I already addressed the issue of how Saul died, there's some interesting language here that may further shed light on the matter. If this is a true story, (and once again, with no corroborating witnesses, this may be a fabrication) then Saul's last words were, "Stand, I pray thee, upon me, and slay me: for anguish is come upon me, because my life is yet whole in me." This indicates to me that Saul wanted to be dead, but wasn't, which may fall in line with my suggestion of a failed suicide. Furthermore, the Amalekite says, "So I stood upon him, and slew him, because I was sure that he could not live after that he was fallen:" which indicates to me that Saul had sustained mortal wounds before the Amalekite got there. Actually, if we assume that the story from the last chapter is true, then this story meshes with it pretty well, and for that fact I'm inclined to believe the Amalekite's tale.
The Amalekite delivers the crown and bracelet that Saul was wearing to David, apparently knowing that these royal things now belong to him, and perhaps hoping to be treated favorably for being the one who killed Saul. David is not pleased, even with it supposedly being a mercy killing, and orders one of his men to kill the Amalekite. I don't really know why David would do this. It may link back to the reasons I formerly discussed as to why David himself refused to lay a finger on Saul. Violent? Definitely. Unjust? I personally agree with that assessment. Intolerant? Maybe if we're assuming that David's killing him at least in part for being an Amalekite.
David composes a little poem as a eulogy for Saul and Jonathan, talking about what great warriors they were, and how Saul made Israel into a great nation. Also, he speaks of the great love he had for Jonathan, which need not be interpreted as sexual love.