A review of Sats tests in England's primary schools is calling for changes to English tests to increase creativity - but with more focus on the basics.
Lord Bew, who led the review of the national curriculum tests taken by 11-year-olds, says a controversial creative writing test should be scrapped.
Teachers should judge children's creative writing, he says, but pupils should still face official tests of spelling, grammar and punctuation as well as reading and maths.
Last year 4,000 schools boycotted Sats, saying they narrowed pupils' education.
Teachers and head teachers in two unions had been calling for the tests to be scrapped.
Heads have given a "cautious welcome" to the findings of the independent review, saying they are "initially encouraged" by it, but one classroom teachers' union has dismissed it as a "fudge".
The coalition government had promised to reform a "flawed" testing system and commissioned this review by Lord Bew, an independent peer and professor of politics at Queen's University, Belfast.
It will announce next month its plans to change the system, but the Education Secretary Michael Gove has already described the review's findings as "educationally sound".
Lord Bew is recommending the current creative writing - or composition - test be replaced by teacher assessment, where a teacher grades a child's work over a year.
He told BBC Radio 4's Today programme his panel hoped this "would allow for more creativity" and mean "less emphasis on drilling and teaching to the test".
But he said it was "important to retain rigour within the system".
External assessments in maths and reading had been "much less criticised" by the teachers his panel had talked to, and these would be retained, he said.
His review also recommends the reading test should be "refined" and that there should be a distinct writing test covering spelling, grammar, punctuation and vocabulary.
The panel said they believed the test would raise attainment in these areas.
Also, these were areas where there were "clear right or wrong answers" - unlike in the creative writing test, which teachers had complained was subjective and difficult to judge consistently.
Critics, including many authors, had complained that the English Sats tests were killing children's natural creativity.
The review also says more data should be published to give a rounded picture of a school's performance, including new measures of the progress of lower-attaining pupils.
Lord Bew recommends a three-year "rolling average" of performance be published.
"What we were constantly told by people that we talked to was, while accountability was desirable, the way it currently operated in some ways provided an unfair snapshot of a school's performance," he said.
Lord Bew is also calling for a greater emphasis on the progress children make from their initial starting points, as well as their overall attainment.
The two should be at least equally weighted in any overall judgement of a school by the government, local authorities or Ofsted, the review recommends.
Lord Bew said the panel believed the changes would lead to a better system, benefit pupils and be fairer to teachers, while still holding schools accountable and giving parents "the vital information they need".
Education Secretary Michael Gove said the proposed changes represented an "educationally sound approach... fair for teachers and schools".
Russell Hobby, the general secretary of the National Association of Head Teachers, said he hoped any changes might "reduce the tyranny of the league table" - but that much would depend on how the government interpreted the findings.
"We are pleased to see the professionalism of school leaders recognised and greater trust placed in teachers as the best judges of pupil progress," he said.
"We are particularly encouraged that Lord Bew has recommended teacher assessment for writing and that far greater weight be given to teacher assessment overall.
"This will reduce drilling and give both parents and secondary schools a far more accurate picture of pupils' achievement.
"The move away from crude attainment statistics toward a new focus on pupil progress... is critical.
"It will highlight those schools that do fantastic work in the most challenging circumstances and level the playing field for them."
But the review's findings were criticised by the classroom teachers' union, the NASUWT.
General secretary Chris Keates, said: "The secretary of state would have been wiser to hold fire on accepting the direction of travel of this report given its incoherent nature.
"He has ducked the issue and come up with a fudge.
"[Lord] Bew is claiming to give more trust to teachers but his recommendations, on teacher assessment and making the annual performance tables even more burdensome, will do the opposite."
At the moment, national curriculum tests, or Sats, are taken by children in English and maths.
In addition, schools are required to make statutory teacher assessments in English, maths and science, which are published alongside the test results.
The published Sats results are used by media organisations to create league tables of schools' performances and it is this which many school heads and teachers are opposed to.
Sats tests only exist in England. They were abolished in Wales and Northern Ireland and were never used in Scotland.