Cigarette = папироса/сигарета/сигаретка

[david-us.livejournal.com]

Do these three words refer to something different?
папироса
сигарета
сигаретка

I did a little research and it said that папироса has a cardboard mouthpiece. That seems odd. Are there such cigarettes in Russia? Or, is that referring to a "filter", that is common with American cigarettes?

сигаретка appears to be in some kind of diminutive form. Do they have "little cigarettes", smaller than the average size, in Russia?

Which is more common?

David Emerling
Memphis, TN