It’s beginning to seem as though pretty soon no one will be left holding public office in Israel above the level of a junior high school principal.

The latest head to roll is that of national police chief Moshe Karadi, who resigned on Sunday after a commission investigating the police force’s handling of two murders, one in 1999 of an Israeli underworld figure named Pinchas Buchbut, and the other in 2004 of a policeman who had confessed to being one of the hit men in the Buchbut killing, charged Mr. Karadi with dereliction of duty.

The main accusation against him was that he furthered and approved the promotion of a high police officer despite his knowledge that the officer was probably lying about his ties with Buchbut’s assassins and may have been involved in a cover-up to protect them.

The report of the Zeiler Commission, as it has been called for its chairman, retired judge Vardi Zeiler, did not directly accuse Mr. Karadi of having done anything illegal. In fact, only one of the commission’s three members actually called for his resignation, the other two having been willing to make do with a reprimand. In this respect, the report did little more than make a bit clearer what was already no secret in Israel, namely, that there have for years been connections between the police and the underworld that have not been limited to law enforcement.

This is not, needless to say, a uniquely Israeli phenomenon. Police deal with criminals as routinely as immunologists deal with microbes, and the chances of infection are always great.

The problem in a highly centralized country like Israel, as opposed, say, to that in America, is that there is no such thing as local police departments; one national force with headquarters in Jerusalem polices the entire nation. In some respects, this tends to minimize corruption, for which local police unsupervised by higher authorities can be notorious. Yet on the other hand, it makes corruption far more serious when it occurs, since the infection is then in the entire body rather than in just a finger or a toe.

Whether or not the kind of fraternizing, if not worse, that exists in Israel between elements in the underworld and in the police can be rooted out under new leadership is something that will not become evident immediately. In the short run, Mr. Karadi’s resignation may have its greatest repercussions not on the police, but on the political future of Ehud Olmert.

Like Mr. Karadi, Mr. Olmert has also testified before a commission of inquiry, the Winograd Commission, which has been entrusted with investigating the failures of last summer’s military campaign against Hezbollah in Lebanon. Like Mr. Karadi, too, no one is accusing him of doing anything illegal. Not in regard to Lebanon, anyway — Mr. Olmert’s legal problems these days lie elsewhere. And as turned out to be the case with the Zeiler Commission, no one expects the Winograd Commission, however harshly critical it may be of his handling of last summer’s war, to call for Mr. Olmert’s resignation.

But if the Winograd Commission does come down as hard on Mr. Olmert as the Zeiler Commission did on Mr. Karadi, Mr. Olmert is going to find Mr. Karadi’s precedent hard to ignore. How will he explain to the nation that, while his chief of police had enough sense of responsibility to resign when accused of gross negligence in the case of a single murder, he, a prime minister accused of botching an entire war, is not resigning?

And how, especially, will he explain it when former chief of staff Dan Halutz, the army’s commander during the Lebanese war, has already resigned without waiting for the Winograd Commission’s report?

Hezbollah head Hassan Nasrallah is not making things easier for Mr. Olmert either. In an incident not widely reported by the international press, Mr. Nasrallah addressed his followers in Beirut last week after the Lebanese army had intercepted a truck full of munitions on its way to Hezbollah fighters in southern Lebanon — an action expressly forbidden by Security Council Resolution 1701, which ended last summer’s war. In a defiant speech, the Hezbollah leader announced that his organization has indeed been resupplying its forces in the south all along and has every intention of continuing to do so, despite the U.N. resolution to which it was a party.

In testifying before the Winograd Commission, it has been said, Mr. Olmert defended the war against Hezbollah by claiming that, despite shortcomings in its execution, it was a success because it resulted in the elimination of Hezbollah as a fighting force along Israel’s northern border.

Now, along comes Mr. Nasrallah in person and says that this fighting force not only still exists, it is being militarily beefed up all the time while U.N. forces stationed in Lebanon are there to prevent it and say nothing. If this is Mr. Olmert’s idea of a success, one is certainly glad the war was not a failure. There is still time, one assumes, for the Winograd Commission to quote Mr. Nasrallah in its report.

A preliminary version of the commission’s report is expected to be issued within a few weeks. If Ehud Olmert does not come out looking reasonably well in it, his days are probably numbered. He already has the lowest approval rate of any prime minister in the history of polling in Israel, and his standing in his own party, Kadima, which itself may not hold together for very much longer, is slipping badly too.

He may not survive the Winograd Commission’s report any more than Moshe Karadi survived the Zeiler Commission’s.

Mr. Halkin is a contributing editor of The New York Sun.