Abstract. We improve a criterion of Inkeri and show that if there is a solution to Catalan's equationwith p and q prime numbers greater than 3 and both congruent to 3 (mod 4), then p and q form a double Wieferich pair. Further, we refine a result of Schwarz to obtain similar criteria when only one of the exponents is congruent to 3 (mod 4). Indeed, in light of the results proved here it is reasonable to suppose that if q ≡ 3 (mod 4), then p and q form a double Wieferich pair.