We prove a new `runner removal theorem' for $q$-decomposition numbers of the
level 1 Fock space of type $A^{(1)}_{e-1}$, generalising earlier theorems of
James--Mathas and the author. By combining this with another theorem relating
to the Mullineux map, we show that the problem of finding all $q$-decomposition
numbers indexed by partitions of a given weight is a finite computation.