UNABLE TO MAINTAIN ALT ACCOUNT MOUNTAIN WAVE AND GROSS WEIGHT OF ACFT.

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WE WERE CLRD FROM FL350 TO FL390. OVER HILL CITY VOR AT APPROX 370; CENTER ASKED IF WE COULD BE LEVEL FL390 IN 4 MINS. WE SAID YES. I ADJUSTED CLB RATE ON AUTOPLT TO APPROX 600 FPM. AS WE CLBED; OUR SPD DETERIORATED FROM .82 MACH TO .77. AS WE LEVELED OFF; SPD FELL FURTHER TO .725 (225 KTS). WE ALSO SEEMED TO ENCOUNTER A MTN WAVE. WE HAD SELECTED MCT ON THE AUTOTHROTTLES; BUT WE COULD BARELY MAINTAIN SPD. I PUNCHED OFF AUTOTHROTTLES AND AUTOPLT; BUT COULD NOT MAINTAIN SPD AND ALT. WE ENCOUNTERED LIGHT TO MODERATE CHOP AND ALT DECREASED TO FL386 BEFORE WE COULD GET CLRNC TO FL370. THERE WAS TFC RIGHT BELOW US AT FL370. WE FINALLY TURNED AND DESCENDED WHICH SOLVED THE PROB. WE DID; HOWEVER; ENCOUNTER LOW SPD BUFFET AND CAME VERY CLOSE TO STALLING AT FL390; WHICH WOULD HAVE BEEN UNHEALTHY; TO SAY THE LEAST. THIS ACFT HAS THE CHARACTERISTIC OF SORT OF DYING IN THE LAST FEW THOUSAND FEET OF CLB. I KNEW THIS; AND SHOULD HAVE TOLD CENTER THAT I COULD NOT MAINTAIN CLB RATE. THIS PUT US VERY CLOSE TO THE BACK SIDE OF THE PWR CURVE. THE MTN WAVE DID THE REST. NEXT TIME I WON'T BE SO HELPFUL AND TAKE A VECTOR FOR CLB AS NECESSARY. ACCORDING TO THE BOOK; WE WERE LEGAL FOR THE ALT. AT OUR WT; WE NEEDED .82-.83 MACH; HOWEVER. SUPPLEMENTAL INFORMATION FROM ACN 81176: AS WE LEVELED OFF AT FL390 WE HIT A MTN WAVE ACTIVITY AND TURBULENCE WITH THE SPD FALLING OFF TO .725 MACH (225 KTS). AT THIS POINT WE SELECTED MAX COUNT PWR (MCT). THE SPD STILL WAS DETERIORATING AND TO TRY TO MAINTAIN SPD BECAUSE WE WERE SO CLOSE TO A STALL OUR ALT WENT DOWN TO 38600' AND ENCOUNTERED A LOW SPD BUFFET. SUPPLEMENTAL INFORMATION FROM ACN 81377: WE REQUESTED LOWER ALT AND ACFT SEEMED TO BE GETTING CLOSER TO A LOW SPD BUFFET. CENTER TURNED US 40 DEGS AND APPROVED FL370. ALT HAD DECREASED DURING ALL THIS TO FL386 BEFORE CENTER HAD CLRD US DOWN TO FL370.