Now that President Barack Obama has secured more than enough votes in the U.S. Senate to assure the implementation of the agreement with Iran on nuclear issues and sanctions, we can focus on the lessons learned from the process’ intense political dynamics.

These dynamics have affected three relationships: that between the United States and Israel; between the U.S. and Saudi Arabia along with the Gulf Cooperation Council; and between the GCC and Iran. Bilateral U.S.-Israeli ties have garnered the most attention these days, but all three are equally important, and turbulent in their own ways.

The agreement with Iran heightened sensitivities all around, and significantly increased the fears of Israel and the GCC states about Iranian capabilities and intentions. History will determine if these fears are justified or wildly exaggerated (I see them as exaggerated); today we can only assess the implications of the dynamics during the past two years.

The American and Israeli media are full of accounts of the fallout of Israeli Prime Minister Benjamin Netanyahu’s all-out effort in the United States Congress and media to thwart the agreement’s approval in Congress. That effort failed and left behind considerable irritation, and some anger, among Americans who felt that Israel went too far in its attempt to manipulate American foreign policy. Most damaging was Israel’s very public campaign to turn American members of Congress against their own president’s determination of the best interests of the United States.

I suspect the core, strong strategic and emotional bonds between the U.S. and Israel will remain unchanged. Political men and women – as is their vocation – will quickly put ill feelings behind them as they seek allies and assets for the next election. Obama will increase U.S. military and technical assistance for Israel’s security needs, showing that he disagrees with Netanyahu but is committed to the security of Israel. None of this is new, so none of it is important either.

What is new and important is that the Israeli prime minister, with his substantial number of American allies and assorted instruments of influencing American public opinion (like pro-Israel lobby groups and policy institutes in Washington) lost a battle that he said related to the existence of Israel, and lost it in a very public manner. This confirms two basic truths that we have long known: Israel has extraordinary influence in the U.S. Congress; but also the American president can defeat the pro-Israel lobby groups when he takes his case to the American people. None of this is new, either.

I do see some noteworthy aspects here, though. Some American members of Congress and other public figures felt uncomfortable, even offended, that they were being asked to choose between supporting their own president or the Israeli prime minister. The appropriate response to this is essentially, “tough luck.” According to the rules and laws of politics in America, all interested parties are free to lobby for their views, using votes, money, congressional visits, fear-mongering, advertising, and public speeches. Lobby groups for Israel or others will digest this lesson and perhaps be more subtle in their activities in future.

More troubling, many American Jews will be uncomfortable if they feel that because of the political actions of fellow Jews in Israel, they will be seen as Americans with divided loyalties. This always creates openings for vile anti-Semitic attacks, which should be thwarted by all available means because they are a catastrophe for all concerned.

Another unclear aspect of this experience is how pro-Israel lobby groups, including American Christians, might adjust their behavior in the U.S. following this defeat. Some of this may be clarified in the behavior of such groups toward American members of Congress who supported the Iran deal. Will these groups – as some of them have done in the past – try to defeat vulnerable incumbent congressmen or women by supporting pro-Israel candidates? This, too, would be totally normal and legal in the world of American politics and public life. So anyone who dislikes this process is best advised to learn how to play the game and get in the ring – with the confirmation that American special interests groups that support Israel are not all-powerful, and can be defeated in a public battle.

The two other important dimensions of the Iran agreement – Saudi and GCC relations with the U.S. and Iran – are more complex, and conducted almost totally behind closed doors. So perhaps one lesson here is that Saudi Arabia and the other Arab Gulf states, who find their wellbeing more closely tied to the interests and policies of both the U.S. and Iran, should come out of the shadows and start to master the mechanics of public politics and diplomacy around the world.