I use cotton pads with Baby oil and for stubborn areas, a Q-tip soaked with Baby oil. I find that baby oil leaves my eye area a lot smoother than makeup removers, and I've also stopped shedding lashes.
Agree with the qtip comment. Use cotton pad for bigger swoop above and below eye and then qtip closer to eye for better control. Also- try easing up on the amount of product to avoid any drip...this is what I find irritate my eyes!