We revisit the well known discrepancy between the observed number of Milky Way ( MW ) dwarf satellite companions and the predicted population of cold dark matter ( CDM ) sub-halos , in light of the dozen new low luminosity satellites found in imaging data from the Sloan Digital Sky Survey ( SDSS ) and our recent calibration of the SDSS satellite detection efficiency , which implies a total satellite population far larger than these dozen discoveries . We combine a detailed dynamical model for the CDM sub-halo population with simple , physically motivated prescriptions for assigning a stellar content to each sub-halo , then apply observational selection effects and compare to the current observational census . Reconciling the observed satellite population with CDM predictions still requires strong mass-dependent suppression of star formation in low mass sub-halos : models in which the stellar mass is a constant fraction F _ { * } ( \Omega _ { b } / \Omega _ { m } ) of the sub-halo mass M _ { sat } at the time it becomes a satellite fail for any choice of F _ { * } . However , previously advocated models that invoke suppression of gas accretion after reionization in halos with circular velocity V _ { circ } \leq V _ { crit } \approx 35 { km~ { } s } ^ { -1 } can reproduce the observed satellite counts for -15 \leq M _ { V } \leq 0 . Successful models require F _ { * } \approx 10 ^ { -3 } in halos with V _ { circ } > V _ { crit } and strong suppression of star formation before reionization in halos with V _ { circ } \lesssim 10 { km~ { } s } ^ { -1 } ; models without pre-reionization suppression predict far too many satellites with -5 \leq M _ { V } \leq 0 . In this successful model , the dominant fraction of stars formed after reionization at all luminosities . Models that match the satellite luminosity distribution also match the observed heliocentric radius distribution , and they reproduce the observed characteristic stellar velocity dispersion \sigma _ { * } \approx 5 - 10 { km~ { } s } ^ { -1 } of the SDSS dwarfs given the observed sizes ( \sim 50 - 200 pc ) of their stellar distributions . The model satellites have M ( < 300 { pc } ) \sim 10 ^ { 7 } M _ { \odot } as observed even though their present day total halo masses span more than two orders of magnitude ; the constancy of central masses mainly reflects the profiles of CDM halos . Our modeling shows that natural physical mechanisms acting within the CDM framework can quantitatively explain the properties of the MW satellite population as it is presently known , thus providing a convincing solution to the ‘ missing satellite ’ problem .