Oil is up more than 30 percent since its low in March and one oil policy expert thinks it's going to continue to move higher.
Kent Moors, executive chair of the Global Energy Symposium, said he sees "restrained upside moving forward." He's predicting a gradual increase to about $70-$73 per barrel for and $60-$65 for U.S. crude by mid-July.
"We're going to be reaching a major point in the midsummer where peak in production from the primary new wells 12-18 months in the past is going to be hit, which means we are going to see a rather significant decline in production from the newest wells," Moors said in an interview with "Closing Bell."
"What we are going to be seeing is a ratcheting up of the pricing floor as the new supply and demand balances kick in."
Moors also thinks prices will continue to move higher through the end of the year, noting that Brent could go over $80 by December.
However, Neal Dingmann, energy analyst at SunTrust Robinson Humphrey, thinks near-term prices are going to fall.
He said the drop in rig counts by about half this year is only part of the reason for the recent jump in oil prices.
"You've really had a sharp cutoff on new wells coming online," he said.
Dingmann said the number of wells that have been drilled but are not completed are at about eight to 10 times more than average.
"If oil hits $60 you are immediately going to have a lot of these unconventional U.S. wells come on very quickly," Dingmann told "Closing Bell."
He also said Saudi Arabia plans to continue its strong production and thinks Libya and Iran don't appear as the imminent threats they were perceived to be a couple of months ago.
—CNBC's Stephen Desaulniers contributed to this report.