If you break down the word sinecure, you can pretty easily discover what it means etymologically. It never was a single word until English (today it means "an easy but well-paid job"); in Latin it was a phrase, beneficium sine cura (somehow the former word got lost in translation), meaning "benefice without care", basically today's definition. Just the sine cura means "without care", reflecting the simplicity of the task. Sine, which we see in sin- ("without"), goes back to Proto-Indo-European swe, "self", and it developed on the sense of "stand alone". Cura you may recognize as being similar to the word cure. This is for good reason; it is the direct etymon of that word; the shared definition is "concern", which makes sense for both venues. This is from Proto-Indo-European kwes, or "to heed". So, if you're truly without caring, in the future you'll call a sinecure "heeding yourself".
Adam Aleksic, a leading contender for valedictorian of his high school, is a 214-month-old boy with disturbing interests in etymology, vexillology, geography, and law. Adam would like to one day visit Tajikistan and probably isn't spying for the Uzbek government.
The Etymology Nerd