Given PSPACE $\ne$ EXP, is there a non-PSPACE-hard language in EXP - PSPACE?
The proof of Ladner's theorem doesn't use any special properties of P and NP and the same proof unchanged will show, assuming EXP&lt;>PSPACE, there is a language L in EXP-PSPACE and not EXP-complete under either P-time or PSPACE-reductions.

You need the full Landner look-back trick to keep L in EXP.