By Chris Isidore, CNN

(CNN) — Oil futures tumbled again Tuesday on hopes that the shaky ceasefire between Israel and Iran would reduce if not eliminate the risk any significant disruption to global energy markets. Gasoline futures fell, too.

So when will you notice prices falling at the pump?

It may be a while. Because gas prices didn’t shoot significantly higher over the past two weeks after Israel and Iran began their recent hostilities, you probably won’t notice any big savings anytime soon.

The national average gasoline price stood at $3.12 on June 10 according to AAA, just before oil and gasoline prices started their climb on rising concerns about a conflict in the days before the fighting started between Israel and Iran. The so-called New York harbor prices for gasoline futures closed at a wholesale price of only $2.09. A barrel of Brent crude, the global benchmark for oil closed at $66.60 that day.

Both wholesale gasoline and oil futures stared rising steadily June 11 and continued to climb through the early hours of trading this past Sunday night, after the US bombing of nuclear sites in Iran raised fears of a broader conflict. Brent Crude futures briefly topped $80 a barrel late Sunday.

But throughout the day Monday as those fears of a wider conflict retreated and hopes for a cease fire increased, the price of oil started falling sharply.

Oil Monday closed down 7% at $70.65 a barrel, while a so-called New York harbor prices for gasoline futures fell about 5% to a wholesale price of $2.22 a gallon. And the wholesale prices fell another 5% in midday trading Tuesday to a $2.09 price, essentially matching the price before the recent run-up.

The AAA average retail price for a gallon of regular gasoline stood Monday at $3.22, based on a survey of gas stations conducted on Sunday, and it remains there in Tuesday’s reading.

But that means there was only a 3% rise in pump prices from June 10 to today’s level, so there’s not a lot of room for prices to fall to go back to pre-conflict levels.

Tom Kloza, an independent oil and gasoline price expert, said he could see prices starting to decline a little bit in the coming days as stations take deliveries of cheaper wholesale gas.

The seasonal pick-up in summer driving will stop prices from falling significantly in the coming weeks, he believes. But he does think that a glut of oil on global markets and strong US refining capacity could send prices down sharply through the rest of this year once the peak July demand wanes.

“It looks like we’re well supplied, and that’s bearish for prices,” he said.

The strong supply has little to do with President Donald Trump’s “drill, baby, drill” call to increase production. Overall US production is roughly unchanged from this time last year and it’s not likely to increase significantly at the current prices, Kloza said, especially with 50% tariffs on imported steel raising the cost of the pipes used in oil exploration.

The price of oil futures did not spike as high as during some past global incidents, such as Russia’s attack on Ukraine and the imposition of sanctions on Russia by western nations that followed. In that case Brent prices soared 44% from early January 2022 through early March of that year. But Kloza said there isn’t as much speculative money in oil futures markets as there used to driving up prices in reaction to external events.

“That money is much more likely to go into crypto and to go into big tech today,” he said. “There’s only so much money to go around.”

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