Air carrier Captain reported severe mountain wave and aircraft over speed during cruise. Crew requested lower altitude and conditions approved.

Narrative

At FL350 approaching ALS there were reports of chop and mountain wave turbulence from ATC and Dispatch. Seatbelt sign was illuminated and flight attendants told to take their jumpseats. About 30 miles west of PUB we began to experience light turbulence. PF opened the speed intervention window and reduced mach number from .77 to .76. Shortly after indicated airspeed began to quickly increase. Speed brakes were deployed to the full inflight position and power reduced to idle but airspeed continued to uncontrollably increase. Mach number and indicated airspeed increased above VMO and the clacker began to sound for about 10 seconds. Mach number increased to approximately .84 with an airspeed gain of around 40 knots and altitude gains of 200 to 300 feet occurred.Airspeed then began to suddenly decrease and moderate turbulence with 20 degrees of bank occurred. As indicated airspeed approached the low speed band the autopilot was disconnected and speed brakes stowed but airspeed continued to be uncontrollable. PF pushed to decrease aircraft pitch and added thrust. PM notified ATC of severe mountain wave and the need for an immediate descent which was approved to FL 290. Descending through FL320 aircraft flight path and airspeed became controllable again. We continued descent to FL 290 where the autopilot was engaged and only light chop was encountered.PIREP was passed to ATC and Dispatch. Flight attendants were told to check in and reported no injuries or damage sustained in the cabin. An ELB (Electronic Log Book) entry was sent to Maintenance Control and flight continued to destination without further incident.