Narrative:

I was PIC flying west in the vicinity of zzzzz intersection. I received descent instructions out of FL470 for what I remember was for FL290. The center requested that I expedite below FL340. I increased my rate of vertical speed. The TCAS advisory (TA) sounded and I noted that I had about seven NM separation and 700 ft vertical on oncoming (one o'clock) traffic. At that data point I was at 34;300 ft and the traffic was at FL350. Simultaneously; center told an aircraft to turn left to 075 degrees. I believe it was an air carrier flight; but I cannot be certain about the call sign. Whoever it was; they were probably cruising east at FL350. I take responsibility for not expediting as fast as the controller needed me too. I remember thinking that I need to hurry; but that I did not need to bounce anybody off the cabin ceiling. I should have used 1200 FPM down on the initial start of the descent (slowly increasing to 2400 FPM) approaching FL290. Early on in descent; I was expecting to hear center tell me something like 'cross 60 NM east of ZZZ below FL340.' at the relevant time; the sic was trying to call ahead to our destination and to also obtain ATIS. I recall paying some attention to how that was going. However; in my opinion; the controller was conscientious about his traffic separation and relied on what he knows to be the 'norm' for his descents.

Related reports:

Google
 

Original NASA ASRS Text

Title: A corporate jet descending for an ATC requested expedited descent from FL470 to FL290 experienced a TCAS TA at FL343. The reporter acknowledged the descent may have been at a slower rate than expected by ATC.

Narrative: I was PIC flying west in the vicinity of ZZZZZ intersection. I received descent instructions out of FL470 for what I remember was for FL290. The Center requested that I expedite below FL340. I increased my rate of vertical speed. The TCAS advisory (TA) sounded and I noted that I had about seven NM separation and 700 FT vertical on oncoming (one o'clock) traffic. At that data point I was at 34;300 FT and the traffic was at FL350. Simultaneously; Center told an aircraft to turn left to 075 degrees. I believe it was an air carrier flight; but I cannot be certain about the call sign. Whoever it was; they were probably cruising east at FL350. I take responsibility for not expediting as fast as the controller needed me too. I remember thinking that I need to hurry; but that I did not need to bounce anybody off the cabin ceiling. I should have used 1200 FPM down on the initial start of the descent (slowly increasing to 2400 FPM) approaching FL290. Early on in descent; I was expecting to hear Center tell me something like 'Cross 60 NM east of ZZZ below FL340.' At the relevant time; the SIC was trying to call ahead to our destination and to also obtain ATIS. I recall paying some attention to how that was going. However; in my opinion; the controller was conscientious about his traffic separation and relied on what he knows to be the 'norm' for his descents.

Data retrieved from NASA's ASRS site as of April 2012 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.