A pure falsetto, one with no admixture of chest register, cannot be sustained; the vocal cords are not fully adducted. The sound produced is hooty, like the cooing of a dove. Here is a test. Sing a note in the lower part of your range—mezzo forte—and sustain it on the vowel ah. Stop. Utter a few iterations of falsetto on oo, short and very hooty. There is no need to blast air, but air will nonetheless be released. Make no attempt to sustain it. Now, return to that recently sung note in the chest. Has it changed? If so, you have used the function of the falsetto to isolate that of the chest register. Bravo. The falsetto is an effective tool for this purpose, isolating and refining the chest register, pushing the pieces off the board and starting over for the day or a practice session. It cancels over-refinement. I hope you’ll want to try this.