This paper presents two fully polynomial-time sufficient feasibility tests for EDF when considering periodic tasks with arbitrary deadlines and preemptive scheduling on uniprocessors. Both proposed methods are proven, analytically and by means of an extensive experimental comparison, to be more accurate than known polynomial-time feasibility tests. Additionally, we show for a wide interval of practical processor utilization that one of these methods presents almost the same efficiency, in terms of accepted task sets, as the more complex pseudo-polynomial-time exact feasibility tests.