Instead of key stage 2 and 3 pupils being tested on years of work in one all-or-nothing week in May, the exam load would be spread. Pupils would take a test at a single, national curriculum level when their teacher believed they were ready to pass it.
There would be two testing "windows", in December and June. If they failed a test, they could retake it. In theory, seven-year-olds could take the same test as 14-year-olds. This would support personalised learning.
Many teachers welcomed the tests, including their greatest selling point: the reduction of pressure on pupils. The fact that they get several chances to pass suggests children can relax a bit.
However, problems with the results generated by the first set of tests six weeks ago - in trials at 411 schools - are highlighting difficulties. The most fundamental is the problem that, at each level, one test is supposed to assess the progress of both primary and secondary pupils.
Yet the curriculums they have been taught are different in both maths and English. The original idea of Sats tests - that pupils are taught the national curriculum and then examined on it - has therefore been lost.
The new tests also place demands on both teachers and the test designers. Teachers must get their assessment judgements right in order to choose correctly when to enter pupils for a test. This has been identified by Ofsted as a weakness throughout the profeession.
Educationally, the biggest danger is reductionism. Fifty-minute tests can sample even less of the curriculum than is possible under the longer Sats exams.
The worry, with the new tests to contribute to league tables and targets, is even more narrowly focused teaching.
Sats tests remain unpopular, a fact even the Government acknowledges in the Children's Plan. And teething problems are to be expected in a pilot. But it seems unwise for ministers to have put so much faith in this model of when-ready testing already, instead of using it to explore different approaches.
Even more urgently, the Government must acknowledge the deeper concerns about the effects of its testing regime on children. It should respond with an independent inquiry.