  We investigate two invariants of Noetherian semiperfect rings, namely the
depth and a new invariant we call the "delooping level". These give lower and
upper bounds for the finitistic dimension, respectively. As first theorems, we
give a necessary and sufficient criterion for the delooping level to be finite
in terms of the splitting of the unit map of a related adjunction, and use this
to give a sufficient torsionfreeness criterion for finiteness. We further
relate these invariants to the Auslander-Bridger grade conditions for modules,
which are vanishing conditions on double Ext duals. As main theorem, we prove
that these bounds agree whenever the first non-trivial grade conditions are
satified for simple modules, so that either invariant computes the finitistic
dimension in this case. Over Artinian rings, we show that the delooping level
also bounds the big finitistic dimension, and we obtain a sufficient
cohomological criterion for the first finitistic dimension conjecture to hold.
Over commutative local Noetherian rings, these conditions always hold and we
obtain a new characterisation of the depth as the delooping level of the ring.
