We analyze a sample of 58 Oort cloud comets (OCCs) (original orbital energies x in the range 0 < x < 100, in units of 10−6 AU−1), plus 45 long-period comets with negative orbital energies or poorly determined or undetermined x, discovered during the period 1999-2007. To analyze the degree of completeness of the sample, we use Everhart's (1967 Astr. J 72, 716) concept of “excess magnitude” (in magnitudes × days), defined as the integrated magnitude excess that a given comet presents over the time above a threshold magnitude for detection. This quantity is a measure of the likelihood that the comet will be finally detected. We define two sub-samples of OCCs: 1) new comets (orbital energies 0 < x < 30) as those whose perihelia can shift from outside to the inner planetary region in a single revolution; and 2) inner cloud comets (orbital energies 30 ≤ x < 100), that come from the inner region of the Oort cloud, and for which external perturbers (essentially galactic tidal forces and passing stars) are not strong enough to allow them to overshoot the Jupiter-Saturn barrier. From the observed comet flux and making allowance for missed discoveries, we find a flux of OCCs brighter than absolute total magnitude 9 of ≃0.65 ± 0.18 per year within Earth's orbit. From this flux, about two-thirds corresponds to new comets and the rest to inner cloud comets. We find striking differences in the q-distribution of these two samples: while new comets appear to follow an uniform q-distribution, inner cloud comets show an increase in the rate of perihelion passages with q.