The so-called Aten asteroids, evolving on orbits with semimajor axis a<1 AU and aphelion distance Q>0.983 AU, spend most of their time inside Earth's orbit. Currently, they account for about 7% of the observed near-Earth asteroid population and 13% of the Earth-crossing one. However, observational biases play against their discovery; thus the present number of Atens is probably severely underestimated. Another still unobserved population of asteroids, which we call IEO (inner-Earth objects), could also exist and evolve entirely inside Earth's orbit. Orbital numerical integrations of known source populations of Earth-crossers indicate that the real fraction of Atens and IEOs in the Earth-crossing population depends on the considered objects' diameters and could be close to 20% considering only the multikilometer bodies. Moreover, the fraction of IEOs could be as large as half that of Atens. Since these asteroids can also impact Earth, their threat should seriously be taken into account.