  It has long been hypothesised that the Jupiter-family comets (JFCs) come from
the scattered disc, an unstable planetesimal population beyond Neptune. This
viewpoint has been widely accepted, but a few issues remain, the most prominent
of which are the total number of visible JFCs with a perihelion distance q<2.5
AU and the corresponding number of objects in the scattered disc. In this work
we give a robust estimate of the number of visible JFCs with q<2.5 AU and
diameter D>2.3 km based on recent observational data. This is combined with
numerical simulations that use a simple fading law applied to JFCs that come
close to the Sun. For this we numerically evolve thousands of comets from the
scattered disc 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 JFC inclination and semi-major axis distribution accurately with a delayed
power law fading function and the maximum perihelion distance below which the
observational data is complete is q~2.3 AU. From observational data we
calculate that a JFC with diameter D=2.3 km has a typical total absolute
magnitude H_T=10.8, and the steady-state number of active JFCs with diameter
D>2.3 km and q<2.5 AU is of the order of 300 (but with large uncertainties),
approximately a factor two higher than earlier estimates. The increased JFC
population results in a scattered disc population of 6 billion objects and
decreases the observed Oort cloud to scattered disc population ratio to 13,
virtually the same as the value of 12 obtained with numerical simulations.
