(Lieven < MO, 2/05/2018):  QIl v. "be desperate", as when there's no way out, they have nothing to lose. This includes ideas like last-ditch, do-or-die, hopeless, doomed.

(Lieven < MO, 2/07/2018):  My interpretation of desperate in the third sentence ('You were desperate to save us') is a little different.  Here I think it means something more like "eager for, longing for, in real need of, having a great desire for" and so on.  For this, you could get by with the suffixes -nIS and -qu':  jutoDnISqu' (or chetoDnISqu'; or perhaps with neHqu':  jutoD DaneHqu' (or chetoD boneHqu').

SEE ALSO:

neH             want (v)
tul             hope (v)
jIn             wish (v)