A verb attested in Qenya Word-lists of the 1920s in a last of rhymes in -alle, with a past for palle “shook” (PE16/143). It might be based on a later variant of the early root ᴱ√PAPA “✱tremble” (PE16/143).
Neo-Quenya: Helge Fauskanger use this as the verb for “to shake” in his NQNT (NQNT), but I prefer [ᴱQ.] quas- as a more distinctive verb for “shake”; see that entry for discussion.
A verb appearing as ᴱQ. qasa- “shake, flap, nod, rustle” in the Qenya Lexicon of the 1910s under the early root ᴱ√QASA (QL/76). Tolkien gave it the past form qasse after which he marked “(intr.)”. This perhaps indicates there was a distinct transitive past (not given), or that the entire verb was intransitive.
Neo-Quenya: I retain ᴺQ. quas- “to shake, flap, nod” for purposes of Neo-Quenya, but assume it is based on a Neo-Root ᴺ√KWATH so that it retains the same modern form. Its classical form would be quaþ-. For “rustle” I would instead use [ᴱQ.] hyasta-.