Apparatus for sorting mixed waste materials, comprising: a first sieve screen having upper and lower surfaces (300,310) and first sieve openings configured to allow only particles having a maximum dimension less than or equal to a first threshold dimension to pass therethrough; a second sieve screen having upper and lower surfaces (410,420) and second sieve openings configured to allow only particles having a maximum dimension less than or equal to a second threshold dimension to pass therethrough, the second threshold dimension being less than the first threshold dimension; and a third surface; wherein the apparatus is configured such that particles passing through the first sieve screen fall under gravity towards the upper surface of the second sieve screen and particles passing through the second sieve screen fall under gravity towards the third surface; the apparatus being further configured to generate: a first gas stream between the lower surface of the first sieve screen and the upper surface of the second sieve screen and configured to drive off volatile contaminants from particles passing through the first sieve screen, the first gas stream having a respective first velocity; and a second gas stream between the lower surface of the second sieve screen and the third surface and configured to drive off volatile contaminants from particles passing through the second sieve screen, the second gas stream having a respective second velocity, less than the first velocity, characterized by: dampers configured to control the velocity of the first and/or second gas streams (J,K); and a variable-speed fan located upstream of the dampers to simultaneously vary the velocities of both the first and the second gas streams (J,K). a first sieve screen having upper and lower surfaces (300,310) and first sieve openings configured to allow only particles having a maximum dimension less than or equal to a first threshold dimension to pass therethrough; a second sieve screen having upper and lower surfaces (410,420) and second sieve openings configured to allow only particles having a maximum dimension less than or equal to a second threshold dimension to pass therethrough, the second threshold dimension being less than the first threshold dimension; and a third surface; wherein the apparatus is configured such that particles passing through the first sieve screen fall under gravity towards the upper surface of the second sieve screen and particles passing through the second sieve screen fall under gravity towards the third surface; the apparatus being further configured to generate: a first gas stream between the lower surface of the first sieve screen and the upper surface of the second sieve screen and configured to drive off volatile contaminants from particles passing through the first sieve screen, the first gas stream having a respective first velocity; and a second gas stream between the lower surface of the second sieve screen and the third surface and configured to drive off volatile contaminants from particles passing through the second sieve screen, the second gas stream having a respective second velocity, less than the first velocity, characterized by: dampers configured to control the velocity of the first and/or second gas streams (J,K); and a variable-speed fan located upstream of the dampers to simultaneously vary the velocities of both the first and the second gas streams (J,K). a first gas stream between the lower surface of the first sieve screen and the upper surface of the second sieve screen and configured to drive off volatile contaminants from particles passing through the first sieve screen, the first gas stream having a respective first velocity; and a second gas stream between the lower surface of the second sieve screen and the third surface and configured to drive off volatile contaminants from particles passing through the second sieve screen, the second gas stream having a respective second velocity, less than the first velocity, characterized by: dampers configured to control the velocity of the first and/or second gas streams (J,K); and a variable-speed fan located upstream of the dampers to simultaneously vary the velocities of both the first and the second gas streams (J,K). dampers configured to control the velocity of the first and/or second gas streams (J,K); and a variable-speed fan located upstream of the dampers to simultaneously vary the velocities of both the first and the second gas streams (J,K).