Subject to some conditions, the input data for the Drinfeld-Sokolov co
nstruction of KdV-type hierarchies is a quadruplet (A, Lambda, d(1), d
(0)), where the d(i) are Z-gradations of a loop algebra A and Lambda i
s an element of A is a semisimple element of the nonzero d(1)-grade. A
new sufficient condition on the quadruplet under which the constructi
on works is proposed and examples are presented. The proposal relies o
n splitting the d(1)-grade zero part of A into a vector space direct s
um of two subalgebras. This permits one to interpret certain Gelfand-D
ickey-type systems associated with a nonstandard splitting of the alge
bra of pseudodifferential operators in the Drinfeld-Sokolov framework.