The Neutrogena T-Sal is technically sulfate free, but this ingredient is pretty much just as bad as SLS.

Water , Cocamidopropyl Betaine , Sodium C14 16 Olefin Sulfonate , Linoleamidopropyl PG Dimonium Chloride Phosphate , Sodium Lauroyl Sarcosinate , Polyquaternium 22 , Hexylene Glycol , Sodium Citrate

I've actually tried low poos with Sodium C14 16 Olefin Sulfonate that were more drying than SLS poos.

What Makes a Cleansing Ingredient More Harsh or More Gentle?

I wouldn't recommend the Shea Moisture Organic African Black Soap Deep Cleansing Shampoo. I believe the African Black Soap ingredient is a saponified oil and pH level of these soap can destroy the acid mantle of your skin causing you further issues. I used diluted liquid soap on my face was not a smart life decision .
If I'm wrong about what African Black Soap is or if the salicylic acid balances it out...ignore that.

I think the ingredients for the Giovanni Don't Be Flaky! Soothing Anti-Dandruff Shampoo are good.