It took accurate intelligence to know where Nemtsov would be on Friday night, and serious organisation and planning to carry out the killing in such a heavily policed area.
That points to members of the military or security forces, though not necessarily to ones who were acting on official orders. Because, the first thing to say about this murder, is that it did not serve Putin's purposes.
No doubt the Russian president disliked and despised Nemtsov, but neither he nor any other opposition leader posed any threat to Putin's power. Thanks in large part to his seizure of Crimea and his military intervention in eastern Ukraine, Putin is currently enjoying an 85 per cent approval rating with the Russian public.
Why risk upsetting this happy relationship with the first public killing of a senior political figure in more than a decade?
It's much more likely that the killing was carried out by serving or former soldiers or intelligence officers, who took it upon themselves to eliminate an "anti-patriotic" politician who condemned "Putin's War" in Ukraine. In the superheated atmosphere of nationalist paranoia that prevails in Russia, such people could easily imagine that they were doing just what Putin secretly wanted.
Putin is too clever to want that, and immediately condemned the killing as "vile and cynical". It was a curious choice of words: "vile", of course, but why "cynical?"
The reason became clear when various senior regime members began hinting that the murder was a "provocation" by the Western intelligence services or even by Nemtsov's own opposition colleagues, killing him to stimulate dissent and bring the Russian state into disrepute.
As for the rest of the world (or at least the "western" part of the world), it has already written Putin off as a man you can do business with.
The Russian leader is, in many Westerners' eyes, an expansionist warlord who can only be contained by sanctions and threats.
It may even take a new Cold War to stop him. Paranoia, alas, is a communicable disease.
The Western narrative that seeks to explain how, in less than a year, we have arrived at a point where the United States is contemplating supplying heavy weapons to Ukraine to kill Russian troops, has several large gaps.
The first is that the revolution on the Maidan in Kiev last winter overthrew a legitimately elected Ukrainian president only a year before the next elections were due.
Putin initially accepted that outcome (with the elections moved up to only one month in the future), which was brokered by the European Union.
In other words, he accepted the illegal overthrow of the pro-Moscow president, Viktor Yanukovych, so long as free elections followed rapidly.
That same thought may also be why the revolutionaries in Kiev broke the deal and insisted on Yanukovych's immediate removal from power. It was only then that Putin concluded that he was faced with a Western plot to whisk Ukraine into Nato and create a strategic and political threat on Russia's southern frontier.
There was no such plot: Nato has not the slightest desire to assume responsibility for the defence of Ukraine.
But there was a great deal of open Western rejoicing at Russia's discomfiture, and Putin lost his customary cool and responded with the annexation of Crimea and then the encouragement of pro-Russian rebels in southeastern Ukraine.
"Absolute power corrupts absolutely," said Lord Acton. "All great men are bad." In that sense, Putin is a bad man, and more dangerous for being both paranoid and increasingly isolated. (His circle of advisers has dwindled to a handful of hawks.)
But he is not planning to conquer even Ukraine, let alone the rest of the former Soviet empire, and he almost certainly did not order Nemtsov's death.
Gwynne Dyer is an independent journalist whose articles are published in 45 countries.
