But ministers have said that they will not allow schools to opt out of inspections or national tests. The introduction of fees has also been ruled out.
The power to innovate is most likely to be used by schools who do not qualify for earned autonomy (see above) but who still want to make changes to the curriculum. Schools with earned autonomy who want to make radical changes may also apply.
One interesting suggestion is that headteachers might want to apply to ditch most of the curriculum for a short period to concentrate on one particular subject.
Ms Morris would have to be convinced that a school's proposals would lead to higher standards.
The power does not allow schools to opt-out of non-education legislation such as employment law or health and safety regulations.
As with earned autonomy, it is up to schools to initiate any of these changes; ministers cannot demand that they impose them.