FLC OF AN MLG ACR ACFT UNDERSHOT DSCNT ALT RESULTING IN NOT MEETING AN ASSIGNED XING RESTR.

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IT WAS A SHORT LEG FROM IDAHO FALLS TO SALT LAKE CITY; FILED AT A RELATIVELY HIGH ALT OF FL290. WE HAD BEEN CLRED TO FL290 AND DIRECT TO BEARR INTXN UPON FIRST CONTACT WITH THE CTR. I REMEMBER THINKING THAT WE MAY HAVE TO START OUR DSCNT BEFORE REACHING CRUISE ALT IF SLC WAS LNDG TO THE S. WHILE I WAS MAKING THE NORMAL PA ANNOUNCEMENT IN CONJUNCTION WITH TURNING OFF THE SEAT BELT SIGN WE HAD BEEN CLRED TO CROSS BEARR AT 17000 FT. MY FO INFORMED ME OF THIS AND I NOTED THAT THE ALT ALERT WAS STILL SET AT FL290 AS WE WERE STILL CLBING. IT WAS AT THIS TIME THAT OUR ATTN WAS DIVERTED BY A PROB WITH A HYD LOW PRESSURE WARNING LIGHT. THE LIGHT HAD COME ON WITH ALL OTHER PRESSURE AND QUANTITY INDICATIONS NORMAL. WE DECIDED IT WAS AN INDICATION PROB ONLY AND MY FO STARTED CHKING TO FIND THE APPROPRIATE ACARS CODE TO SEND TO ALERT MAINT TO THE NATURE OF THE PROB. JUST AS I STARTED MY DSCNT; CTR CALLED AND REQUESTED OUR ALT. MY FO RESPONDED; 'LEAVING 290.' CTR REPLIED THAT THEY SHOWED US AT 32.3 (NOT CERTAIN OF THE EXACT ALT THEY SHOWED; BUT BELIEVE HE SAID 32.3) AND REQUESTED THAT WE CHK OUR XPONDER AND SWITCH TO ANOTHER IF POSSIBLE. WE VERIFIED OUR ALT; CHKED THE XPONDER SWITCH SETTINGS AND THEN SWITCHED TO THE #2 XPONDER. CTR THEN QUICKLY ASKED; 'ARE YOU GOING TO MAKE BEARR AT 17000 FT?' I GLANCED AT THE DME WHICH INDICATED 54.7 AND TOLD MY FO; 'SURE; WE'LL MAKE IT.' IT HIT ME ALMOST IMMEDIATELY AS I UTTERED THE WORDS; I HAD LOOKED AT THE DME FROM THE OGDEN VOR WHICH WAS ON THE NAV DISPLAY AND NOT AT THE DISTANCE TO BEARR WHICH WAS ON THE OMEGA. I PUT THE AIRCRAFT INTO A MAX DSCNT KNOWING I WAS IN TROUBLE BUT STILL THINKING I HAD A CHANCE TO MAKE THE RESTR UNTIL ANOTHER GLANCE AT THE OMEGA SHOWED THAT THE LESS THAN 40 KT WIND I HAD NOTED EARLIER WAS NOW 116 KTS AND ALMOST DIRECTLY ON THE TAIL. WE CROSSED BEARR AT 22600 FT; NEARLY 6000 FT HIGH AND DROPPING AT BETTER THAN 4000 FPM. IT WAS THE MOST ACUTE FEELING OF HUMILIATION I HAVE EXPERIENCED SINCE JUNIOR HIGH SCHOOL. I BELIEVE WE WERE; FORTUNATELY; THE ONLY TFC IN THE AREA AND THERE WAS NO SAFETY HAZARD -- JUST AN AWKWARD HDOF BTWN ATC FACILITIES. FAULT: MINE COMPLETELY. LESSON LEARNED -- WHEN THERE IS ANY DOUBT; ESPECIALLY IN UNFAMILIAR TERRITORY (FIRST TIME IN AND OUT OF IDA FOR BOTH OF US); AND THE LITTLE VOICE IN THE BACK OF YOUR MIND SAYS; 'MAYBE YOU SHOULD LEVEL AT 250;' DO IT. BE SUPER CONSERVATIVE. CONTRIBUTING FACTORS: CREW FATIGUE. WE HAD BEEN DELAYED 1 HR AND 10 MINS BY WX AT THE HUB ON OUR FIRST LEG OF THE TRIP AND ENDED UP WITH A 12 HR DUTY DAY AND A SHORT LAYOVER OF 9 PLUS 15.