A partimento diminuito is a partimento for which the composer provided one or more models/suggestions of how it can be realized. Those models were incipits —and thus quite short— and not necessarily referring to the first bar(s).
The term first appears in the pedagogical oeuvre of the Neapolitan maestro Francesco Durante (1684–1755). In turn, one of his former students Fedele Fenaroli (1730–1818) wrote five such partimenti but did not name them as such.
See also partimento.