Another area of contention is the disputed oil-rich Maysan border region in southeastern Iraq.
The Iraqi government last month signed a 20-year production contract with a Chinese-Turkish consortium to develop a cluster of three oil fields there that contains the equivalent of 2.6 billion barrels of oil and which both states claim as their own.
A unit of Iran's Islamic Revolutionary Guard Corps occupied an oil well in the Fakka field for two weeks in December, widely seen as a show of force along the poorly defined border.
It's even less defined further north in Kurdistan. Iraq's Kurdish minority has a semi-autonomous enclave there where Iranian Kurdish separatists of the Party for Free Life in Kurdistan, or PEJAK, have bases.
Iraqi officials said 35-40 Iranian troops crossed the border pursuing PEJAK rebels June 2 and set up a base around the mountain village of Perdunaz, 1 mile inside Iraq.
Iranian artillery had been shelling PEJAK positions for several days before the incursion and further incursions are likely to remind Baghdad who's boss.
Similar operations have been conducted by the Iranians in the region in the past but they have rarely, if ever, established a base inside Iraqi territory.
This apparent escalation, however modest, in the wake of the Maysan incursion -- and several others that resulted in exchanges of gunfire -- has raised the stakes along the 800-mile border and underlined the risk of further conflict.
The Shiite regime in Tehran has been making a concerted effort to promote an alliance of Iraqi Shiites, many of them supported by Iran, to form the next government following inconclusive parliamentary elections in March.
With U.S. forces withdrawing from Iraq, a pullout scheduled for completion in late 2011, the Iranians want to ensure that postwar Iraq will be subservient, if not directly controlled by Tehran so pressure can be expected to increase.
The Iranians aren't wild about Iraq's plans to quadruple its oil production over the next several years to 10 million-12 million barrels per day from the current 2.4 million bpd.
This ambitious program -- many in the industry say it's too ambitious -- is heavily dependent on the 11 foreign consortiums Baghdad has brought in to develop its long-battered oil industry over the last year.
The latest deal, to develop the Maysan complex, was with Chinese oil giant CNOOC and Turkey's TPAO.
Iraq has known oil reserves of around 115 billion barrels, the fourth largest after Saudi Arabia, Canada and Iran. But untapped reserves are believed to total as much again, which would put Iraq in the No. 1 spot, eclipsing even Saudi Arabia.
Two-thirds of Iraq's current reserves are in the south, which is dominated by the majority Shiites.
Iran covets those fields and the Fakka incursion in December underlines its determination to prevent Iraq stealing what Iranians consider their oil.
According to Hadi Nejad Hosseinian, a former Iranian deputy oil minister, Tehran has claimed ownership of 20 oil and gas fields along the border.
No hard estimate of the reserves of these fields is available, he said, "but the majority of them are among Iran's biggest fields."
There's a history of oil-grabbing in the region. In September 1980, Saddam Hussein invaded Iran across the southern border into Khuzestan province, center of Iran's oil industry.
A decade later, after ending the 1980-88 war pretty much where he started, Saddam invaded Kuwait to seize its oil fields and was soundly defeated by a U.S.-led coalition.
Iran doesn't want the new, post-Saddam Iraq to threaten its energy industry. Quadrupling Iraqi production could push prices down, which Iran cannot afford.
It oil and gas fields need upgrading and developing as much as Iraq's. International sanctions over the last 30 years have taken their toll, as they did to Iraq's energy industry through lack of access to high-tech equipment or investment.
That may be about to get worse as the United Nations imposes a fourth round of sanctions because of Iran's nuclear program. That's likely to make Iraq's energy riches look mighty tempting.