Let 𝒦 [ C , D ] , − 1 ≤ D < C ≤ 1 , denote the class of functions g ( z ) , g ( 0 ) = g ′ ( 0 ) − 1 = 0 , analytic in the unit disk U = { z : | z | < 1 } such that 1 + ( z g ″ ( z ) / g ′ ( z ) ) is subordinate to ( 1 + C z ) / ( 1 + D z ) , z  ϵ  U . We investigate the subclasses of close-to-convex functions f ( z ) , f ( 0 ) = f ′ ( 0 ) − 1 = 0 , for which there exists g  ϵ  𝒦 [ C , D ] such that f ′ / g ′ is subordinate to ( 1 + A z ) / ( 1 + B z ) , − 1 ≤ B < A ≤ 1 . Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.