In a series of papers Zinger and his collaborators introduced reduced Gromov--Witten invariants. These are numbers which contain fewer degenerate contributions than Gromov--Witten invariants. Together with Luca Battistella and Francesca Carocci we use moduli spaces of stable maps from curves with cusps to define new invariants. We show that for the quintic three-fold these invariants are equal to Zinger's reduced Gromov--Witten invariants.