The origin of the Halley-type comets ( HTCs ) is one of the last mysteries of the dynamical evolution of the Solar System .
Prior investigation into their origin has focused on two source regions : the Oort cloud and the Scattered Disc .
From the former it has been difficult to reproduce the non-isotropic , prograde skew in the inclination distribution of the observed HTCs without invoking a multi-component Oort cloud model and specific fading of the comets .
The Scattered Disc origin fares better but suffers from needing an order of magnitude more mass than is currently advocated by theory and observations .
Here we revisit the Oort cloud origin and include cometary fading .
Our observational sample stems from the JPL catalogue .
We only keep comets discovered and observed after 1950 but place no a priori restriction on the maximum perihelion distance of observational completeness .
We then numerically evolve half a million comets from the Oort cloud through the realm of the giant planets and keep track of their number of perihelion passages with perihelion distance q < 2.5 AU , below which the activity is supposed to increase considerably .
We can simultaneously fit the HTC inclination and semi-major axis distribution very well with a power law fading function of the form m ^ { - k } , where m is the number of perihelion passages with q < 2.5 AU and k is the fading index .
We match both the inclination and semi-major axis distributions when k \sim 1 and the maximum imposed perihelion distance of the observed sample is q _ { m } \sim 1.8 AU .
The value of k is higher than the one obtained for the Long-Period Comets ( LPCs ) , for which typically k \sim 0.7 .
This increase in k is most likely the result of cometary surface processes .
We argue the HTC sample is now most likely complete for q _ { m } < 1.8 AU .
We calculate that the steady-state number of active HTCs with diameter D > 2.3 km and q < 1.8 AU is of the order of 100 .