The head of England's testing watchdog says more than 90% of children could reach the expected level in Sats tests, breaking through a "glass ceiling".
Dr Ken Boston said the way results had hit an attainment plateau at about 80% was an international phenomenon.
He told a committee of MPs current tests were like "Swiss army knives", trying to serve too many purposes.
But personalised learning, more short tests and training for teachers could get performance moving sharply upwards.
Earlier the government formally published for consultation its proposal to split the existing Qualifications and Curriculum Authority (QCA) which Dr Boston runs.
A separate and independent exams regulator would be created, in an effort to reassure everyone that standards were being maintained from year to year.
Dr Boston said people had identified at least 22 legitimate purposes which the current tests taken by all children at the ages of 11 and 14 were trying to serve.
The risk was they did none of them very well.
But he said they were "absolutely fit for purpose for the purpose for which they were designed".
Primarily this was to show the attainment level a child had reached at the end of each "key stage" in their learning.
Optimistic
In this year's tests for 11-year-olds, 80% reached the expected standard in English and 77% in maths.
The conditions for breaking through the international glass ceiling already existed - the difficulty was in bringing them together in the classroom, he told the Children, Schools and Families select committee.
But there now seemed to be a willingness to do that so he was "pretty optimistic about the future".
New "single level tests" have just had their first pilot sitting in more than 400 schools around the country.
These are a check on whether children have reached a specific level for which they are entered.
The idea is that they would be entered for them only when their teachers felt they were ready.
Dr Boston said however: "We need to be thinking not of either/or, I guess that's the message I want to get to.
"We are not thinking of key stage tests or single level tests or sample tests.
"If we want to serve those 22 legitimate purposes - and I'm sure there are more - then we need to use all of these tests."
'Hysteria'
On the splitting of the QCA, ministers said when they proposed it that having an independent regulator would end the "old and sterile debate" about exam standards being "dumbed down".
Asked about the "two weeks of hysteria" around exam results coming out each August, Dr Boston said he did not think that would go away.
But he did think it was right to separate the QCA's functions as was being proposed because the regulatory wing should not be reporting to the organisation that was trying to drive up standards.
Committee chairman Barry Sheerman put it to the QCA chief that he might have been expected to be "sulking" that his organisation was not being asked to carry out the newly-announced review of the primary school curriculum.
Instead, as part of its Children's Plan, the government has asked Sir Jim Rose to undertake the work, albeit with QCA assistance.
Sir Jim produced an earlier report which Mr Sheerman said had gone "totally overboard" in advocating teaching children to read using synthetic phonics.
Mr Sheerman asked if he had been asked to review the curriculum because he was a "political fixer".
"I have no comment on that," said Dr Boston.
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