How can I wash my toddler's hair without traumatizing her?

My 15-month-old gets very upset when it's time to rinse her hair. I've tried several different techniques: laying her on a towel on the vanity and rinsing it in the sink, holding her in the shower, using the rag (but that doesn't work very well). We also have that rinse cup that has the rubber side you place on the child's forehead to keep the water out of her face, but she won't hold still. I don't want her to be afraid of baths/showers but she is and I don't know what else to do. She won't even sit and play in the tub anymore - she stands and holds onto the edge. So I wash her quickly and get her out, but to do that I pretty much have to dump the water over her hair and we both hate that.