well founded
adjective
they have a well-founded fear of persecution if they are deported:
justifiable, justified, warranted, legitimate, defensible, supportable, sustainable, tenable, well grounded, valid, admissible, allowable, understandable, excusable, warrantable, acceptable, reasonable, logical, sensible, sound, just, bona fide, genuine, plausible, credible, believable.
▷antonyms unjustified, groundless.
well founded Oxford Dictionary of English