When I was a lifeguard, I used to teach swimming lessons, and so stories of terrible swimming instructors make me cringe. (I had one or two myself, and pretty much had to learn at my own pace with a bit of coaching from my father.)

Private lessons with a calm, sympathetic instructor can certainly help. I'd offer to give them myself if I were in any geographic position to do so. ^^;; And I think it's worth mentioning the bad experiences to the instructor beforehand -- I once worked with an older man who'd nearly drowned as a child when a cruel cousin threw him into a lake at the family summer home, and he had a profound fear of not being able to touch the bottom. I ended up giving him my lifeguard rescue tube (nice and solid foam) and I actually towed him around the deep end, swimming along beside him and talking him through the feeling of having nothing under his feet. Even if he wasn't swimming on his own, he did have the sense of being more in control in deep water. He wouldn't be swimming the Channel anytime soon, but I do think he felt comfortable enough to not panic when the water was more than chest-high. If he hadn't mentioned that incident to me, though, I wouldn't have been able to tailor my lesson to help him enjoy it.