  Subject to some conditions, the input data for the Drinfeld-Sokolov
construction 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 $\Lambda\in \A$
is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on
the quadruplet under which the construction works is proposed and examples are
presented. The proposal relies on splitting the $d_1$-grade zero part of $\A$
into a vector space direct sum of two subalgebras. This permits one to
interpret certain Gelfand-Dickey type systems associated with a nonstandard
splitting of the algebra of pseudo-differential operators in the
Drinfeld-Sokolov framework.
