From May 3-8, Washington DC hosted a high-powered delegation from the Kurdistan Regional Government (KRG). KRG President Massoud Barzani was flanked by Deputy Prime Minister Qubad Talabani, National Security Chancellor Masrour Barzani and Minister of Peshmerga Affairs Mustapha Sayyid Qadr, among other KRG ministers and officials.

In the three years since Barzani's last White House visit, a lot has changed. Back then, just six months after the withdrawal of US forces, Iraq was a bad memory that the Obama administration wanted to forget. Today Iraq is the key theatre of the war against the self-styled Islamic State of Iraq and the Levant (ISIL).

As important, US-Kurdish relations had frayed badly since Barzani's June 2012 visit. Washington had refused to back a cross-sectarian May 2012 effort, led by Barzani, to oust Prime Minister Nouri al-Maliki.

The Iraqi prime minister then began to send US-equipped federal military forces to the border of Kurdistan and had even told his generals that they might march on Erbil one day but only after the US-built F-16 strike aircraft were delivered to Iraq.

The first such F-16s land in Iraq in mid-July and will be operational over Iraqi skies by the autumn of this year.

Kurdish concerns over arms transfers

Against this backdrop the last nine months have witnessed intensified discontent among Kurdish leaders over the level of US military support to the Peshmerga, Kurdistan's fighting force.

In particular, the Kurds have complained that Washington has allocated too small a proportion of its $1.6bn Iraq Train and Equip Fund (ITEF) assistance to Kurdistan.

Specific complaints range from the amounts of equipment allocated to Kurdistan, most notoriously the transfer to the Kurds of just 25 Mine-Resistant Ambush-Protected (MRAP) vehicles out of 250 allocated to Iraq by the US.

Slow and indirect delivery of US weapons systems is a connected concern. Washington has chosen to funnel most weapons shipments via the federal Iraqi Ministry of Defence, the only entity entitled by US law to sign end-user certificates (EUCs) for the weapons.

The early May visit to Washington DC might have become just another battle in the deepening struggle between Washington and Erbil but the Kurds chose a different approach.

The Kurds believe that the federal government deliberately slows the transfer of such life-saving vehicles from Baghdad to Erbil, and Kurdish officials even privately complain that MRAPs sent to the KRG had been sabotaged while in transit.

In reaction to these views, the House Armed Services Committee of the US Congress introduced clauses into the annual National Defense Authorization Act (NDAA), the Pentagon's budget, in an attempt to protect the Kurds' fair share of US weapons.

The now notorious draft NDAA for Fiscal Year 2016, an early and unratified version of the final legislation, was amended by congress to include a clause (Section 1223) that named the Peshmerga as one of a number of security forces collectively entitled to "not less than 25 percent" of the annual $715m of US support.

Most controversially the amendment would allow the KRG "as a country" to "directly receive assistance from the United States" if Baghdad failed to meet the aforementioned condition, a clause that sparked security threats from Shia militia leaders against US trainers in Iraq.

Kurds step back from the brink

The early May visit to Washington DC might have become just another battle in the deepening struggle between Washington and Erbil but the Kurds chose a different approach. Correctly reading the tea leaves of the US capital, Erbil smartly stepped back from the brink of a damaging foray into US domestic politics.

The pro-Kurdish amendment of the draft NDAA may have gotten Washington's attention, but if pushed to extremes, the bill could ultimately have hurt the Kurdish cause.

Baghdad protested the language, and US Vice President Joe Biden signalled one day before the Kurdish delegation landed that "all US military assistance in the fight against [ISIL] comes at the request of the Government of Iraq and must be coordinated through the Government of Iraq".

Faced with a US administration that would have fiercely defended its prerogatives over operational military matters, Section 1223 of the NDAA was probably destined to be fought over and ultimately deleted before the draft bill faced ratification in the US Senate.

Instead of trying to force the White House to do Kurdistan's bidding through pressure politics, Barzani seems to have adopted a longer-term view in his dealings with the US on defence.

This is unarguably smart because Section 1223 did not give the Kurds a great deal - sharing a quarter of US material collectively with Sunni Arab paramilitary recipients - but it would have soured relations with the Obama administration at a critical time.

You catch more flies with honey

The Iraqi Kurds arrived in Washington DC with an evident intent to strengthen their relations with the US executive branch, not to re-litigate past grievances or open up new fights. This winning approach has been a long time coming.

The tone of the Kurdish visit was positive throughout: Barzani took every opportunity to thank the US government, military, and public for the decisive impact of air strikes and other military support against the ISIL invasion of the KRG in August 2014.

On weapons, Barzani deftly sidestepped the divisive issue of the NDAA by accepting US assurances that "the necessary weapons" would be provided by the US and its partners without seeking to push a prescriptive formula on the White House.

It may have been this flexibility that turned President Barack Obama's scheduled five-minute "drop-by" at the White House Roosevelt Room into an involved hour-long discussion with Barzani on the US-Kurdish relationship.

The Kurds also listened carefully to in-depth US briefings on weapons shipments intended to demonstrate that Washington was - by its admittedly slow standards - moving as rapidly as possible to get military aid to the Kurds.

Likewise, the Pentagon conclusively showed the Kurds that certain allegations - such as federal Iraqi removal of armour from KRG-bound MRAPs - were entirely inaccurate.

Barzani was also consistently positive about his chief executive counterpart in federal Iraq, Prime Minister Haider al-Abbadi.

"We will continue to help him," Barzani told an audience at a Washington think-tank, glossing over the deep misgivings that the Kurds have over Abbadi's intent and capability to deliver on financial and power-sharing promises.

Indeed this suspicion was driven home by a lower-than-expected $445m monthly payment to the Kurds that was revealed while they were in Washington - which the Kurds wisely chose not to publicly criticise until the visit was over.

On the future liberation of Mosul - described by Barzani as the only way to bring about the "strategic defeat" of ISIL - the Kurds promised to "do everything that is asked of us" short of garrisoning Arab areas.

This again was a smart way to tighten relations with the US at a time when Washington still sees the Mosul battle as vital, but when federal Iraqi leaders are gradually backing away from the northern city in favour of operations in Anbar and Salah al-Din that bring more direct protective benefit to Shia central Iraq.

Playing the long game

The Kurdish performance in Washington was that of the team player. Barzani's patient approach was possible in part because he is the most senior Iraqi Kurdish decision-maker, not a subordinate responsible to a higher authority elsewhere.

Barzani laid out the real objective of the visit when he stated "right now the priority is fighting [ISIL], but the process of self-determination will continue".

In the Kurdish view, the visit provided what Iraqi ambassador to Washington, Lukman Faily, calls an "independence health check", a chance to check-in with the Americans regarding their mid-term view of the Kurds' right to self-determination.

The Kurds seem to have received a neutral response from the Americans regarding the "process of self-determination", which they will view as a green light to continue to move incrementally and peacefully towards economic independence and later de jure statehood.

The KRG has strong US Congressional support and they are unlikely to lose it as long as they do not overstrain their influence and wear out their supporters' enthusiasm at too early a stage,

The Kurds also have firm and growing support from the Pentagon, their partner in the fight against ISIL and the operator of a new US mid-term base at Bashir airfield in Harir, Kurdistan.

The remaining hurdles are the White House and National Security Council, both of which will be refreshed in early 2017, and the Baghdad-leaning state department.

By making the US administration's burden in Iraq easier in the near-term, the Kurds seem to be starting to make a play for these remaining allies in the push for autonomy and international recognition.

Michael Knights is the Lafer Fellow at the Washington Institute for Near East Policy. He specialises in the politics and security of Iraq. He has worked in every Iraqi province and most of the country's hundred districts, including periods embedded with Iraq's security forces.

The views expressed in this article are the author's own and do not necessarily reflect Al Jazeera's editorial policy.