Waiting times for passport control at Heathrow are on target to be cut to an "acceptable" 45 minutes, according to immigration minister Damian Green.
He was appearing before the Parliamentary home affairs committee, after chairman Keith Vaz observed "appalling" queues on Monday morning.
Green said he had visited Heathrow Terminal 4 on Tuesday morning and had found "acceptable" waits of under an hour.
He said staff were on target to achieve waiting times of 45 minutes.
The airport would be going into "full Olympics mode" from Sunday, with 500 extra staff and all passport control desks to be manned at peak times, added Green.
Green admitted that Heathrow had endured a "bad April" for queues but "the idea that there are endless long queues day after day would be misleading now".
"Once the Olympics start, every desk will be manned at peak times," he added.
He said about 80% of desks for non-EU passport checks were occupied when he visited Terminal 4 at 7.20am on Tuesday, and the wait was less than an hour although over the 45 minutes target.
"Forty five minutes is acceptable," he told MPs, adding: "It has got better through May and June, but it is still not perfect."
He refused to commit to keep all desks open at peak times after the Olympics: "The problem is not merely an Olympics problem, but it is a specific Olympics commitment."
Green said he wanted to introduce separate lanes for passengers arriving from countries that require intensive pre-boarding checks, such as the US, Japan, New Zealand and Australia.
He said new staff were being trained to meet demand when students began arriving from overseas in September.
"I am very conscious of what needs to happen after the Olympics. That is why we have brought forward retraining of extra staff," he said.
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