SNP MP Mhairi Black has confronted the welfare reform minister over delays in benefits to the vulnerable.
Lord Freud said he suspected the Department of Work and Pensions was delivering an "acceptable performance".
And he defended the time taken to process Personal Independence Payments (PIPs) after Britain's youngest MP challenged him over continuing "really lengthy" delays of up to 11 weeks.
The SNP MP for Paisley and Renfrewshire South told the minister that although waiting times have reduced significantly since last year advice agencies were still talking of delays.
PIPs, which began replacing Disability Living Allowance in 2013, are meant to help the long-term sick and disabled with some of their extra costs.
When asked by the Scots MP about what the causes were of such lengthy delays, Lord Freud said there had been a "dramatic turnaround" in waiting tiems from what he admitted was a "completely unacceptable system".
He insisted that no new claimant waits more than five weeks and said he suspected that "we are now at the level of acceptable performance".
Concerns about how the Department of Work and Pensions deals with PIPs came to a head in June when the High Court ruled a delay in paying welfare benefits to two disable people was unlawful.
Delays of at least nine months for Personal Independence Payments (PIPs) for these "most vulnerable" of people were unreasonable, a judge ruled.
But the court ruled the pair's human rights were not breached, which meant they were not entitled to compensation.
The pair's lawyers said the ruling showed "clear failings" in the system, but ministers said at the time that the situation was improving.
In June there were reportedly 78,700 people waiting to hear if they can claim PIPs, of whom 3,200 had waited more than a year to have their claims processed, and 22,800 had waited more than 20 weeks.
The claimants, known only as Ms C and Mr W, said the delays meant they struggled to pay for food and fuel, and this caused their health to decline.
Ms C, from Kent, who has ME, severe depression and other health problems, waited from September 2013 to October 2014 to have her eligibility assessed.
The court heard she lived a "hand-to-mouth" existence, spending £8 per week on food, and only left her home once a week to visit the supermarket.
Ms Black told Lord Freud at Parliament's work and pensions committee: "Advice agencies report that some claimants are still facing really lengthy waiting times before they can get their PIP claims...talking about 11 weeks people are still experiencing."
Lord Freud said:"In 2014 we had very very lengthy delays which we said was totally unacceptable. We put an immense amount of effort into transforming the situation.
"The Secretary of State put a target that no-one should wait more than 16 weeks. We have now got the average down. No new claimant waits more than five weeks.
"You always get some outlyers but they are for a very good reason. If someone has not been able to attend three or four times, it is very difficult to process their applicaiton. If they went into a care home, or went into care, a hospital, so they weren't there. There are always going to be some particular situations.
"But when you look at the big statistics, that is one of the most dramatic turnarounds from a completely unacceptable system, that i have ever seen in this department or indeed any other.
When Ms Black queried the five week wait quoted by Lord Freud, Andrew Rhodes, the DWP benefits services director, clarified that the average wait time for an assessment is five to six weeks.
But he added: "It's considerably less than the 16 weeks in March. And very very different to the 42 weeks we saw in 2014."
He added: "There will be outlying cases with more complex medical decisions, you need to see a particular specialist or if they don't turn up for an appointment, it will take longer. As soon as we receive the assessment...we will make that decision within nine days and we are consistently doing much better than that."
Ms Black then asked what specific improvements have been made to the process for people who are still currently experiencing 10 or 11 week waiting times.
Lord Freud responded: "I suspect in the ten week period we are looking at complicated situations which just takes longer. I suspect we are now at the level of acceptable performance.
"Where there are outlyers, clearly exceptional outlyers, we get alerted to them, MPs perform a very useful function and they write to us on individual cases and when we are alerted we can look at them because something has gone wrong. "So that's the process that works and indeed the number of letters that we have received, correspondence in this area, invariably from MPs, has dropped very substantially... to a third of the levels we were seeing a year ago."
PIPs are benefit payments to help people aged 16-64 with "some of the extra costs caused by long-term ill-health or a disability".
They are available to employed and unemployed people, and as of June claimants could receive £21.80 to £139.75 a week, depending on how their condition affects them.
From April 2013, PIPs began replacing Disability Living Allowance.
This process is ongoing and the government says everyone who needs to switch to PIPs should have been contacted by late 2017.
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