We report three user studies in which the Lexical Simplification needs of non-native English speakers are investigated. Our analyses feature valuable new insight on the relationship between the non-natives’ notion of complexity and various morphological, semantic and lexical word properties. Some of our findings contradict long-standing misconceptions about word simplicity. The data produced in our studies consists of 211,564 annotations made by 1,100 volunteers, which we hope will guide forthcoming research on Text Simplification for non-native speakers of English.