A Bombardier CRJ-900 pilot reported experiencing a left engine vibration when reaching cruise altitude; resulting in a reduction in thrust; and descent to a lower altitude; before continuing to the destination airport.

Narrative

Upon reaching cruise altitude FL 330; the left engine Fan Vib (Vibration) indicator read 2.9; the vibration could be felt on the yoke and we could hear it. FO remained PF; I ran the QRC/QRH. Because of the excessive vibration; possibility of damage and the need to reduce airspeed and altitude I decided to [request priority handling] with ATC prior to completing the QRH procedure. Before reducing thrust to idle I opted to descend to FL 250 and slow. At FL 250 and 250 KIAS vibrations were 2.0; we reduced left engine to idle IAW (In Accordance With) QRH then increased to normal thrust with no correction to vibration. We reduce the left thrust enough to reduce Vib to 1.7. We were able to maintain altitude and airspeed at this setting without increasing the right engine thrust. I decided to keep the [priority] status with ATC and continue to ZZZ. In the descent vibration decreased. We landed [Runway] XXC; deployed thrust reversers and Vib increased to 1.8; exited the runway; cancelled the [priority handling] and taxied to the gate with no further issues. Notifications were made IAW FOM X.X.XCause: An excessive van vib indication led me to suspect engine damage. I [request priority handling] with ATC; completed to QRH; and continued to land in ZZZ.Suggestion: Review and consider a change to the QRH verbiage. Specifically the caution note between steps XX and YY. I believe that note will potentially cause pilots to skip step XY; in the way it is written. My recommended change would be along the lines of; A reduction to idle thrust at high altitudes may cause a loss of airspeed or altitude. Before initiating step XY ensure aircraft is at a safe altitude"."