I have shown that extending the velocity in model axes increases the computational cost drastically. Scale separation can reduce the cost but remains much more expensive than conventional FWI. I presented an alternative approach to extended FWI by using data space axes. Although the underlying assumptions might make it less accurate than model space extensions in very complex models, the cost is greatly reduced and becomes similar to the cost of conventional FWI. The synthetic Marmousi example showed remarkable results even when the initial model had large errors. The results of this model are comparable to the results of model space extensions but are significantly cheaper in cost.