The crossword solutions for the term 'BARELY WIN, WITH 'OUT'' are EDGE (4 letters) and EKE (3 letters). The term 'barely win' implies that the victory was close or narrow, while the addition of 'WITH 'out'' suggests that the victory was achieved WITH difficulty. The word EDGE can be used to describe a situation where one has a slight advantage over another, while EKE is an informal verb meaning to manage to do something WITH great effort. Therefore, these two words together suggest a situation where someone barely manages to win a difficult battle.